Information on Result #606568

Linear OA(813, 81, F81, 3) (dual of [81, 78, 4]-code or 81-arc in PG(2,81) or 81-cap in PG(2,81)), using Reed–Solomon code RS(78,81)

Mode: Constructive and linear.

Optimality

Show details for fixed k and m, n and k, k and s, k and t, n and m, m and s, m and t, n and s, n and t.

Other Results with Identical Parameters

None.

Depending Results

The following results depend on this result:

ResultThis
result
only
Method
1Linear OA(8172, 531462, F81, 19) (dual of [531462, 531390, 20]-code) [i]Generalized (u, u+v)-Construction
2Linear OA(8156, 531457, F81, 15) (dual of [531457, 531401, 16]-code) [i]
3Linear OA(8152, 531456, F81, 14) (dual of [531456, 531404, 15]-code) [i]
4Linear OA(8182, 178, F81, 72) (dual of [178, 96, 73]-code) [i]Construction X with Algebraic-Geometric Codes
5Linear OA(8181, 178, F81, 71) (dual of [178, 97, 72]-code) [i]
6Linear OA(8180, 178, F81, 70) (dual of [178, 98, 71]-code) [i]
7Linear OA(8179, 178, F81, 69) (dual of [178, 99, 70]-code) [i]
8Linear OA(8178, 178, F81, 68) (dual of [178, 100, 69]-code) [i]
9Linear OA(8177, 178, F81, 67) (dual of [178, 101, 68]-code) [i]
10Linear OA(8176, 178, F81, 66) (dual of [178, 102, 67]-code) [i]
11Linear OA(8175, 178, F81, 65) (dual of [178, 103, 66]-code) [i]
12Linear OA(8174, 178, F81, 64) (dual of [178, 104, 65]-code) [i]
13Linear OA(8173, 178, F81, 63) (dual of [178, 105, 64]-code) [i]
14Linear OA(8172, 178, F81, 62) (dual of [178, 106, 63]-code) [i]
15Linear OA(8171, 178, F81, 61) (dual of [178, 107, 62]-code) [i]
16Linear OA(8170, 178, F81, 60) (dual of [178, 108, 61]-code) [i]
17Linear OA(8169, 178, F81, 59) (dual of [178, 109, 60]-code) [i]
18Linear OA(8168, 178, F81, 58) (dual of [178, 110, 59]-code) [i]
19Linear OA(8167, 178, F81, 57) (dual of [178, 111, 58]-code) [i]
20Linear OA(8166, 178, F81, 56) (dual of [178, 112, 57]-code) [i]
21Linear OA(8165, 178, F81, 55) (dual of [178, 113, 56]-code) [i]
22Linear OA(8164, 178, F81, 54) (dual of [178, 114, 55]-code) [i]
23Linear OA(8163, 178, F81, 53) (dual of [178, 115, 54]-code) [i]
24Linear OA(8162, 178, F81, 52) (dual of [178, 116, 53]-code) [i]
25Linear OA(8161, 178, F81, 51) (dual of [178, 117, 52]-code) [i]
26Linear OA(8160, 178, F81, 50) (dual of [178, 118, 51]-code) [i]
27Linear OA(8159, 178, F81, 49) (dual of [178, 119, 50]-code) [i]
28Linear OA(8158, 178, F81, 48) (dual of [178, 120, 49]-code) [i]
29Linear OA(8157, 178, F81, 47) (dual of [178, 121, 48]-code) [i]
30Linear OA(8156, 178, F81, 46) (dual of [178, 122, 47]-code) [i]
31Linear OA(8155, 178, F81, 45) (dual of [178, 123, 46]-code) [i]
32Linear OA(8154, 178, F81, 44) (dual of [178, 124, 45]-code) [i]
33Linear OA(8153, 178, F81, 43) (dual of [178, 125, 44]-code) [i]
34Linear OA(8152, 178, F81, 42) (dual of [178, 126, 43]-code) [i]
35Linear OA(8151, 178, F81, 41) (dual of [178, 127, 42]-code) [i]
36Linear OA(8150, 178, F81, 40) (dual of [178, 128, 41]-code) [i]
37Linear OA(8149, 178, F81, 39) (dual of [178, 129, 40]-code) [i]
38Linear OA(8148, 178, F81, 38) (dual of [178, 130, 39]-code) [i]
39Linear OA(8147, 178, F81, 37) (dual of [178, 131, 38]-code) [i]
40Linear OA(8146, 178, F81, 36) (dual of [178, 132, 37]-code) [i]
41Linear OA(8145, 178, F81, 35) (dual of [178, 133, 36]-code) [i]
42Linear OA(8144, 178, F81, 34) (dual of [178, 134, 35]-code) [i]
43Linear OA(8143, 178, F81, 33) (dual of [178, 135, 34]-code) [i]
44Linear OA(8142, 178, F81, 32) (dual of [178, 136, 33]-code) [i]
45Linear OA(8141, 178, F81, 31) (dual of [178, 137, 32]-code) [i]
46Linear OA(8140, 178, F81, 30) (dual of [178, 138, 31]-code) [i]
47Linear OA(8139, 178, F81, 29) (dual of [178, 139, 30]-code) [i]
48Linear OA(8138, 178, F81, 28) (dual of [178, 140, 29]-code) [i]
49Linear OA(8137, 178, F81, 27) (dual of [178, 141, 28]-code) [i]
50Linear OA(8136, 178, F81, 26) (dual of [178, 142, 27]-code) [i]
51Linear OA(8135, 178, F81, 25) (dual of [178, 143, 26]-code) [i]
52Linear OA(8134, 178, F81, 24) (dual of [178, 144, 25]-code) [i]
53Linear OA(8133, 178, F81, 23) (dual of [178, 145, 24]-code) [i]
54Linear OA(8132, 178, F81, 22) (dual of [178, 146, 23]-code) [i]
55Linear OA(8131, 178, F81, 21) (dual of [178, 147, 22]-code) [i]
56Linear OA(8130, 178, F81, 20) (dual of [178, 148, 21]-code) [i]
57Linear OA(8129, 178, F81, 19) (dual of [178, 149, 20]-code) [i]
58Linear OA(8128, 178, F81, 18) (dual of [178, 150, 19]-code) [i]
59Linear OA(8127, 178, F81, 17) (dual of [178, 151, 18]-code) [i]
60Linear OA(8126, 178, F81, 16) (dual of [178, 152, 17]-code) [i]
61Linear OA(8125, 178, F81, 15) (dual of [178, 153, 16]-code) [i]
62Linear OA(8124, 178, F81, 14) (dual of [178, 154, 15]-code) [i]
63Linear OA(8182, 376, F81, 63) (dual of [376, 294, 64]-code) [i]
64Linear OA(8181, 376, F81, 62) (dual of [376, 295, 63]-code) [i]
65Linear OA(8180, 376, F81, 61) (dual of [376, 296, 62]-code) [i]
66Linear OA(8179, 376, F81, 60) (dual of [376, 297, 61]-code) [i]
67Linear OA(8178, 376, F81, 59) (dual of [376, 298, 60]-code) [i]
68Linear OA(8177, 376, F81, 58) (dual of [376, 299, 59]-code) [i]
69Linear OA(8176, 376, F81, 57) (dual of [376, 300, 58]-code) [i]
70Linear OA(8175, 376, F81, 56) (dual of [376, 301, 57]-code) [i]
71Linear OA(8174, 376, F81, 55) (dual of [376, 302, 56]-code) [i]
72Linear OA(8173, 376, F81, 54) (dual of [376, 303, 55]-code) [i]
73Linear OA(8172, 376, F81, 53) (dual of [376, 304, 54]-code) [i]
74Linear OA(8171, 376, F81, 52) (dual of [376, 305, 53]-code) [i]
75Linear OA(8170, 376, F81, 51) (dual of [376, 306, 52]-code) [i]
76Linear OA(8169, 376, F81, 50) (dual of [376, 307, 51]-code) [i]
77Linear OA(8168, 376, F81, 49) (dual of [376, 308, 50]-code) [i]
78Linear OA(8167, 376, F81, 48) (dual of [376, 309, 49]-code) [i]
79Linear OA(8166, 376, F81, 47) (dual of [376, 310, 48]-code) [i]
80Linear OA(8165, 376, F81, 46) (dual of [376, 311, 47]-code) [i]
81Linear OA(8164, 376, F81, 45) (dual of [376, 312, 46]-code) [i]
82Linear OA(8163, 376, F81, 44) (dual of [376, 313, 45]-code) [i]
83Linear OA(8162, 376, F81, 43) (dual of [376, 314, 44]-code) [i]
84Linear OA(8161, 376, F81, 42) (dual of [376, 315, 43]-code) [i]
85Linear OA(8160, 376, F81, 41) (dual of [376, 316, 42]-code) [i]
86Linear OA(8159, 376, F81, 40) (dual of [376, 317, 41]-code) [i]
87Linear OA(8158, 376, F81, 39) (dual of [376, 318, 40]-code) [i]
88Linear OA(8157, 376, F81, 38) (dual of [376, 319, 39]-code) [i]
89Linear OA(8156, 376, F81, 37) (dual of [376, 320, 38]-code) [i]
90Linear OA(8155, 376, F81, 36) (dual of [376, 321, 37]-code) [i]
91Linear OA(8154, 376, F81, 35) (dual of [376, 322, 36]-code) [i]
92Linear OA(8153, 376, F81, 34) (dual of [376, 323, 35]-code) [i]
93Linear OA(8152, 376, F81, 33) (dual of [376, 324, 34]-code) [i]
94Linear OA(8151, 376, F81, 32) (dual of [376, 325, 33]-code) [i]
95Linear OA(8150, 376, F81, 31) (dual of [376, 326, 32]-code) [i]
96Linear OA(8149, 376, F81, 30) (dual of [376, 327, 31]-code) [i]
97Linear OA(8148, 376, F81, 29) (dual of [376, 328, 30]-code) [i]
98Linear OA(8147, 376, F81, 28) (dual of [376, 329, 29]-code) [i]
99Linear OA(8146, 376, F81, 27) (dual of [376, 330, 28]-code) [i]
100Linear OA(8145, 376, F81, 26) (dual of [376, 331, 27]-code) [i]
101Linear OA(8144, 376, F81, 25) (dual of [376, 332, 26]-code) [i]
102Linear OA(8182, 304, F81, 67) (dual of [304, 222, 68]-code) [i]
103Linear OA(8181, 304, F81, 66) (dual of [304, 223, 67]-code) [i]
104Linear OA(8180, 304, F81, 65) (dual of [304, 224, 66]-code) [i]
105Linear OA(8179, 304, F81, 64) (dual of [304, 225, 65]-code) [i]
106Linear OA(8178, 304, F81, 63) (dual of [304, 226, 64]-code) [i]
107Linear OA(8177, 304, F81, 62) (dual of [304, 227, 63]-code) [i]
108Linear OA(8176, 304, F81, 61) (dual of [304, 228, 62]-code) [i]
109Linear OA(8175, 304, F81, 60) (dual of [304, 229, 61]-code) [i]
110Linear OA(8174, 304, F81, 59) (dual of [304, 230, 60]-code) [i]
111Linear OA(8173, 304, F81, 58) (dual of [304, 231, 59]-code) [i]
112Linear OA(8172, 304, F81, 57) (dual of [304, 232, 58]-code) [i]
113Linear OA(8171, 304, F81, 56) (dual of [304, 233, 57]-code) [i]
114Linear OA(8170, 304, F81, 55) (dual of [304, 234, 56]-code) [i]
115Linear OA(8169, 304, F81, 54) (dual of [304, 235, 55]-code) [i]
116Linear OA(8168, 304, F81, 53) (dual of [304, 236, 54]-code) [i]
117Linear OA(8167, 304, F81, 52) (dual of [304, 237, 53]-code) [i]
118Linear OA(8166, 304, F81, 51) (dual of [304, 238, 52]-code) [i]
119Linear OA(8165, 304, F81, 50) (dual of [304, 239, 51]-code) [i]
120Linear OA(8164, 304, F81, 49) (dual of [304, 240, 50]-code) [i]
121Linear OA(8163, 304, F81, 48) (dual of [304, 241, 49]-code) [i]
122Linear OA(8162, 304, F81, 47) (dual of [304, 242, 48]-code) [i]
123Linear OA(8161, 304, F81, 46) (dual of [304, 243, 47]-code) [i]
124Linear OA(8160, 304, F81, 45) (dual of [304, 244, 46]-code) [i]
125Linear OA(8159, 304, F81, 44) (dual of [304, 245, 45]-code) [i]
126Linear OA(8158, 304, F81, 43) (dual of [304, 246, 44]-code) [i]
127Linear OA(8157, 304, F81, 42) (dual of [304, 247, 43]-code) [i]
128Linear OA(8156, 304, F81, 41) (dual of [304, 248, 42]-code) [i]
129Linear OA(8155, 304, F81, 40) (dual of [304, 249, 41]-code) [i]
130Linear OA(8154, 304, F81, 39) (dual of [304, 250, 40]-code) [i]
131Linear OA(8153, 304, F81, 38) (dual of [304, 251, 39]-code) [i]
132Linear OA(8152, 304, F81, 37) (dual of [304, 252, 38]-code) [i]
133Linear OA(8151, 304, F81, 36) (dual of [304, 253, 37]-code) [i]
134Linear OA(8150, 304, F81, 35) (dual of [304, 254, 36]-code) [i]
135Linear OA(8149, 304, F81, 34) (dual of [304, 255, 35]-code) [i]
136Linear OA(8148, 304, F81, 33) (dual of [304, 256, 34]-code) [i]
137Linear OA(8147, 304, F81, 32) (dual of [304, 257, 33]-code) [i]
138Linear OA(8146, 304, F81, 31) (dual of [304, 258, 32]-code) [i]
139Linear OA(8145, 304, F81, 30) (dual of [304, 259, 31]-code) [i]
140Linear OA(8144, 304, F81, 29) (dual of [304, 260, 30]-code) [i]
141Linear OA(8143, 304, F81, 28) (dual of [304, 261, 29]-code) [i]
142Linear OA(8142, 304, F81, 27) (dual of [304, 262, 28]-code) [i]
143Linear OA(8141, 304, F81, 26) (dual of [304, 263, 27]-code) [i]
144Linear OA(8140, 304, F81, 25) (dual of [304, 264, 26]-code) [i]
145Linear OA(8139, 304, F81, 24) (dual of [304, 265, 25]-code) [i]
146Linear OA(8138, 304, F81, 23) (dual of [304, 266, 24]-code) [i]
147Linear OA(8137, 304, F81, 22) (dual of [304, 267, 23]-code) [i]
148Linear OA(8136, 304, F81, 21) (dual of [304, 268, 22]-code) [i]
149Linear OA(8182, 506, F81, 53) (dual of [506, 424, 54]-code) [i]
150Linear OA(8181, 506, F81, 52) (dual of [506, 425, 53]-code) [i]
151Linear OA(8180, 506, F81, 51) (dual of [506, 426, 52]-code) [i]
152Linear OA(8179, 506, F81, 50) (dual of [506, 427, 51]-code) [i]
153Linear OA(8178, 506, F81, 49) (dual of [506, 428, 50]-code) [i]
154Linear OA(8177, 506, F81, 48) (dual of [506, 429, 49]-code) [i]
155Linear OA(8176, 506, F81, 47) (dual of [506, 430, 48]-code) [i]
156Linear OA(8175, 506, F81, 46) (dual of [506, 431, 47]-code) [i]
157Linear OA(8174, 506, F81, 45) (dual of [506, 432, 46]-code) [i]
158Linear OA(8173, 506, F81, 44) (dual of [506, 433, 45]-code) [i]
159Linear OA(8172, 506, F81, 43) (dual of [506, 434, 44]-code) [i]
160Linear OA(8171, 506, F81, 42) (dual of [506, 435, 43]-code) [i]
161Linear OA(8170, 506, F81, 41) (dual of [506, 436, 42]-code) [i]
162Linear OA(8169, 506, F81, 40) (dual of [506, 437, 41]-code) [i]
163Linear OA(8182, 531457, F81, 27) (dual of [531457, 531375, 28]-code) [i]Construction X with Cyclic Codes
164Linear OA(8176, 531457, F81, 25) (dual of [531457, 531381, 26]-code) [i]
165Linear OA(8170, 531457, F81, 23) (dual of [531457, 531387, 24]-code) [i]
166Linear OA(8164, 531457, F81, 21) (dual of [531457, 531393, 22]-code) [i]
167Linear OA(8158, 531457, F81, 19) (dual of [531457, 531399, 20]-code) [i]
168Linear OA(8152, 531457, F81, 17) (dual of [531457, 531405, 18]-code) [i]
169Linear OA(8146, 531457, F81, 15) (dual of [531457, 531411, 16]-code) [i]
170Linear OA(8140, 531457, F81, 13) (dual of [531457, 531417, 14]-code) [i]
171Linear OA(8134, 531457, F81, 11) (dual of [531457, 531423, 12]-code) [i]
172Linear OA(8128, 531457, F81, 9) (dual of [531457, 531429, 10]-code) [i]
173Linear OA(8180, 6573, F81, 39) (dual of [6573, 6493, 40]-code) [i]
174Linear OA(8176, 6573, F81, 37) (dual of [6573, 6497, 38]-code) [i]
175Linear OA(8172, 6573, F81, 35) (dual of [6573, 6501, 36]-code) [i]
176Linear OA(8168, 6573, F81, 33) (dual of [6573, 6505, 34]-code) [i]
177Linear OA(8164, 6573, F81, 31) (dual of [6573, 6509, 32]-code) [i]
178Linear OA(8160, 6573, F81, 29) (dual of [6573, 6513, 30]-code) [i]
179Linear OA(8156, 6573, F81, 27) (dual of [6573, 6517, 28]-code) [i]
180Linear OA(8152, 6573, F81, 25) (dual of [6573, 6521, 26]-code) [i]
181Linear OA(8148, 6573, F81, 23) (dual of [6573, 6525, 24]-code) [i]
182Linear OA(8144, 6573, F81, 21) (dual of [6573, 6529, 22]-code) [i]
183Linear OA(8140, 6573, F81, 19) (dual of [6573, 6533, 20]-code) [i]
184Linear OA(8136, 6573, F81, 17) (dual of [6573, 6537, 18]-code) [i]
185Linear OA(8132, 6573, F81, 15) (dual of [6573, 6541, 16]-code) [i]
186Linear OA(8128, 6573, F81, 13) (dual of [6573, 6545, 14]-code) [i]
187Linear OA(8124, 6573, F81, 11) (dual of [6573, 6549, 12]-code) [i]
188Linear OA(8120, 6573, F81, 9) (dual of [6573, 6553, 10]-code) [i]
189Linear OA(8158, 419, F81, 31) (dual of [419, 361, 32]-code) [i]
190Linear OA(8176, 419, F81, 41) (dual of [419, 343, 42]-code) [i]
191Linear OA(8179, 531456, F81, 26) (dual of [531456, 531377, 27]-code) [i]Construction X with Extended Narrow-Sense BCH Codes
192Linear OA(8173, 531456, F81, 24) (dual of [531456, 531383, 25]-code) [i]
193Linear OA(8167, 531456, F81, 22) (dual of [531456, 531389, 23]-code) [i]
194Linear OA(8161, 531456, F81, 20) (dual of [531456, 531395, 21]-code) [i]
195Linear OA(8155, 531456, F81, 18) (dual of [531456, 531401, 19]-code) [i]
196Linear OA(8149, 531456, F81, 16) (dual of [531456, 531407, 17]-code) [i]
197Linear OA(8143, 531456, F81, 14) (dual of [531456, 531413, 15]-code) [i]
198Linear OA(8137, 531456, F81, 12) (dual of [531456, 531419, 13]-code) [i]
199Linear OA(8131, 531456, F81, 10) (dual of [531456, 531425, 11]-code) [i]
200Linear OA(8125, 531456, F81, 8) (dual of [531456, 531431, 9]-code) [i]
201Linear OA(8182, 6572, F81, 40) (dual of [6572, 6490, 41]-code) [i]
202Linear OA(8178, 6572, F81, 38) (dual of [6572, 6494, 39]-code) [i]
203Linear OA(8174, 6572, F81, 36) (dual of [6572, 6498, 37]-code) [i]
204Linear OA(8170, 6572, F81, 34) (dual of [6572, 6502, 35]-code) [i]
205Linear OA(8166, 6572, F81, 32) (dual of [6572, 6506, 33]-code) [i]
206Linear OA(8162, 6572, F81, 30) (dual of [6572, 6510, 31]-code) [i]
207Linear OA(8158, 6572, F81, 28) (dual of [6572, 6514, 29]-code) [i]
208Linear OA(8154, 6572, F81, 26) (dual of [6572, 6518, 27]-code) [i]
209Linear OA(8150, 6572, F81, 24) (dual of [6572, 6522, 25]-code) [i]
210Linear OA(8146, 6572, F81, 22) (dual of [6572, 6526, 23]-code) [i]
211Linear OA(8142, 6572, F81, 20) (dual of [6572, 6530, 21]-code) [i]
212Linear OA(8138, 6572, F81, 18) (dual of [6572, 6534, 19]-code) [i]
213Linear OA(8134, 6572, F81, 16) (dual of [6572, 6538, 17]-code) [i]
214Linear OA(8130, 6572, F81, 14) (dual of [6572, 6542, 15]-code) [i]
215Linear OA(8126, 6572, F81, 12) (dual of [6572, 6546, 13]-code) [i]
216Linear OA(8122, 6572, F81, 10) (dual of [6572, 6550, 11]-code) [i]
217Linear OA(8118, 6572, F81, 8) (dual of [6572, 6554, 9]-code) [i]