Information on Result #609757

Linear OA(83, 10, F8, 3) (dual of [10, 7, 4]-code or 10-arc in PG(2,8) or 10-cap in PG(2,8)), using hyperoval in PG(2, 8)

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.

Compare with Markus Grassl’s online database of code parameters.

Other Results with Identical Parameters

None.

Depending Results

The following results depend on this result:

ResultThis
result
only		Method
1Linear OA(822, 523, F8, 7) (dual of [523, 501, 8]-code) [i](u, u+v)-Construction
2Linear OA(829, 8204, F8, 7) (dual of [8204, 8175, 8]-code) [i]
3Linear OA(834, 32779, F8, 7) (dual of [32779, 32745, 8]-code) [i]
4Linear OA(841, 524300, F8, 7) (dual of [524300, 524259, 8]-code) [i]
5Linear OA(846, 2097163, F8, 7) (dual of [2097163, 2097117, 8]-code) [i]
6Linear OA(819, 522, F8, 6) (dual of [522, 503, 7]-code) [i]
7Linear OA(825, 8202, F8, 6) (dual of [8202, 8177, 7]-code) [i]
8Linear OA(829, 32778, F8, 6) (dual of [32778, 32749, 7]-code) [i]
9Linear OA(835, 524298, F8, 6) (dual of [524298, 524263, 7]-code) [i]
10Linear OA(839, 2097162, F8, 6) (dual of [2097162, 2097123, 7]-code) [i]
11Linear OA(829, 8206, F8, 7) (dual of [8206, 8177, 8]-code) [i]
12Linear OA(825, 8206, F8, 6) (dual of [8206, 8181, 7]-code) [i]
13Linear OA(876, 83, F8, 58) (dual of [83, 7, 59]-code) [i]Juxtaposition
14Linear OA(8133, 140, F8, 106) (dual of [140, 7, 107]-code) [i]
15Linear OA(812, 29, F8, 7) (dual of [29, 17, 8]-code) [i](u, u−v, u+v+w)-Construction
16Linear OA(836, 32788, F8, 7) (dual of [32788, 32752, 8]-code) [i]
17Linear OA(848, 2097172, F8, 7) (dual of [2097172, 2097124, 8]-code) [i]
18Linear OA(8102, 2097163, F8, 17) (dual of [2097163, 2097061, 18]-code) [i]Construction X with Cyclic Codes
19Linear OA(8172, 262155, F8, 33) (dual of [262155, 261983, 34]-code) [i]
20Linear OA(888, 262155, F8, 17) (dual of [262155, 262067, 18]-code) [i]
21Linear OA(8144, 32779, F8, 33) (dual of [32779, 32635, 34]-code) [i]
22Linear OA(874, 32779, F8, 17) (dual of [32779, 32705, 18]-code) [i]
23Linear OA(8172, 4107, F8, 49) (dual of [4107, 3935, 50]-code) [i]
24Linear OA(8116, 4107, F8, 33) (dual of [4107, 3991, 34]-code) [i]
25Linear OA(860, 4107, F8, 17) (dual of [4107, 4047, 18]-code) [i]
26Linear OA(8172, 523, F8, 63) (dual of [523, 351, 64]-code) [i]
27Linear OA(8166, 523, F8, 61) (dual of [523, 357, 62]-code) [i]
28Linear OA(8160, 523, F8, 59) (dual of [523, 363, 60]-code) [i]
29Linear OA(8154, 523, F8, 57) (dual of [523, 369, 58]-code) [i]
30Linear OA(8148, 523, F8, 55) (dual of [523, 375, 56]-code) [i]
31Linear OA(8142, 523, F8, 53) (dual of [523, 381, 54]-code) [i]
32Linear OA(8130, 523, F8, 47) (dual of [523, 393, 48]-code) [i]
33Linear OA(8124, 523, F8, 45) (dual of [523, 399, 46]-code) [i]
34Linear OA(8118, 523, F8, 43) (dual of [523, 405, 44]-code) [i]
35Linear OA(8112, 523, F8, 41) (dual of [523, 411, 42]-code) [i]
36Linear OA(8106, 523, F8, 39) (dual of [523, 417, 40]-code) [i]
37Linear OA(8100, 523, F8, 37) (dual of [523, 423, 38]-code) [i]
38Linear OA(888, 523, F8, 31) (dual of [523, 435, 32]-code) [i]
39Linear OA(882, 523, F8, 29) (dual of [523, 441, 30]-code) [i]
40Linear OA(876, 523, F8, 27) (dual of [523, 447, 28]-code) [i]
41Linear OA(870, 523, F8, 25) (dual of [523, 453, 26]-code) [i]
42Linear OA(864, 523, F8, 23) (dual of [523, 459, 24]-code) [i]
43Linear OA(858, 523, F8, 21) (dual of [523, 465, 22]-code) [i]
44Linear OA(846, 523, F8, 15) (dual of [523, 477, 16]-code) [i]
45Linear OA(840, 523, F8, 13) (dual of [523, 483, 14]-code) [i]
46Linear OA(844, 75, F8, 25) (dual of [75, 31, 26]-code) [i]
47Linear OA(840, 75, F8, 23) (dual of [75, 35, 24]-code) [i]
48Linear OA(827, 75, F8, 14) (dual of [75, 48, 15]-code) [i]
49Linear OA(831, 75, F8, 16) (dual of [75, 44, 17]-code) [i]
50Linear OA(851, 75, F8, 32) (dual of [75, 24, 33]-code) [i]
51Linear OA(8127, 595, F8, 38) (dual of [595, 468, 39]-code) [i]
52Linear OA(8131, 595, F8, 39) (dual of [595, 464, 40]-code) [i]
53Linear OA(829, 75, F8, 15) (dual of [75, 46, 16]-code) [i]Construction XX with Cyclic Codes
54Linear OA(842, 82, F8, 22) (dual of [82, 40, 23]-code) [i]
55Linear OA(844, 82, F8, 23) (dual of [82, 38, 24]-code) [i]
56Linear OA(843, 77, F8, 24) (dual of [77, 34, 25]-code) [i]
57Linear OA(842, 75, F8, 24) (dual of [75, 33, 25]-code) [i]
58Linear OA(844, 80, F8, 24) (dual of [80, 36, 25]-code) [i]
59Linear OA(843, 78, F8, 24) (dual of [78, 35, 25]-code) [i]
60Linear OA(861, 97, F8, 31) (dual of [97, 36, 32]-code) [i]
61Linear OA(863, 97, F8, 32) (dual of [97, 34, 33]-code) [i]
62Linear OA(856, 87, F8, 31) (dual of [87, 31, 32]-code) [i]
63Linear OA(858, 87, F8, 32) (dual of [87, 29, 33]-code) [i]
64Linear OA(872, 87, F8, 48) (dual of [87, 15, 49]-code) [i]
65Linear OA(825, 525, F8, 8) (dual of [525, 500, 9]-code) [i]
66Linear OA(827, 529, F8, 9) (dual of [529, 502, 10]-code) [i]
67Linear OA(830, 529, F8, 10) (dual of [529, 499, 11]-code) [i]
68Linear OA(828, 524, F8, 10) (dual of [524, 496, 11]-code) [i]
69Linear OA(829, 526, F8, 10) (dual of [526, 497, 11]-code) [i]
70Linear OA(833, 529, F8, 11) (dual of [529, 496, 12]-code) [i]
71Linear OA(831, 524, F8, 11) (dual of [524, 493, 12]-code) [i]
72Linear OA(832, 528, F8, 11) (dual of [528, 496, 12]-code) [i]
73Linear OA(833, 530, F8, 11) (dual of [530, 497, 12]-code) [i]
74Linear OA(836, 529, F8, 12) (dual of [529, 493, 13]-code) [i]
75Linear OA(835, 528, F8, 12) (dual of [528, 493, 13]-code) [i]
76Linear OA(836, 530, F8, 12) (dual of [530, 494, 13]-code) [i]
77Linear OA(841, 537, F8, 13) (dual of [537, 496, 14]-code) [i]
78Linear OA(844, 537, F8, 14) (dual of [537, 493, 15]-code) [i]
79Linear OA(848, 529, F8, 17) (dual of [529, 481, 18]-code) [i]
80Linear OA(850, 526, F8, 18) (dual of [526, 476, 19]-code) [i]
81Linear OA(849, 524, F8, 18) (dual of [524, 475, 19]-code) [i]
82Linear OA(853, 526, F8, 19) (dual of [526, 473, 20]-code) [i]
83Linear OA(852, 524, F8, 19) (dual of [524, 472, 20]-code) [i]
84Linear OA(854, 530, F8, 19) (dual of [530, 476, 20]-code) [i]
85Linear OA(853, 528, F8, 19) (dual of [528, 475, 20]-code) [i]
86Linear OA(857, 529, F8, 20) (dual of [529, 472, 21]-code) [i]
87Linear OA(856, 526, F8, 20) (dual of [526, 470, 21]-code) [i]
88Linear OA(857, 530, F8, 20) (dual of [530, 473, 21]-code) [i]
89Linear OA(856, 528, F8, 20) (dual of [528, 472, 21]-code) [i]
90Linear OA(862, 537, F8, 21) (dual of [537, 475, 22]-code) [i]
91Linear OA(865, 537, F8, 22) (dual of [537, 472, 23]-code) [i]
92Linear OA(869, 529, F8, 25) (dual of [529, 460, 26]-code) [i]
93Linear OA(871, 526, F8, 26) (dual of [526, 455, 27]-code) [i]
94Linear OA(870, 524, F8, 26) (dual of [524, 454, 27]-code) [i]
95Linear OA(874, 526, F8, 27) (dual of [526, 452, 28]-code) [i]
96Linear OA(873, 524, F8, 27) (dual of [524, 451, 28]-code) [i]
97Linear OA(875, 530, F8, 27) (dual of [530, 455, 28]-code) [i]
98Linear OA(874, 528, F8, 27) (dual of [528, 454, 28]-code) [i]
99Linear OA(878, 529, F8, 28) (dual of [529, 451, 29]-code) [i]
100Linear OA(877, 526, F8, 28) (dual of [526, 449, 29]-code) [i]
101Linear OA(878, 530, F8, 28) (dual of [530, 452, 29]-code) [i]
102Linear OA(877, 528, F8, 28) (dual of [528, 451, 29]-code) [i]
103Linear OA(883, 537, F8, 29) (dual of [537, 454, 30]-code) [i]
104Linear OA(886, 537, F8, 30) (dual of [537, 451, 31]-code) [i]
105Linear OA(890, 529, F8, 33) (dual of [529, 439, 34]-code) [i]
106Linear OA(892, 526, F8, 34) (dual of [526, 434, 35]-code) [i]
107Linear OA(891, 524, F8, 34) (dual of [524, 433, 35]-code) [i]
108Linear OA(895, 526, F8, 35) (dual of [526, 431, 36]-code) [i]
109Linear OA(894, 524, F8, 35) (dual of [524, 430, 36]-code) [i]
110Linear OA(896, 530, F8, 35) (dual of [530, 434, 36]-code) [i]
111Linear OA(895, 528, F8, 35) (dual of [528, 433, 36]-code) [i]
112Linear OA(899, 529, F8, 36) (dual of [529, 430, 37]-code) [i]
113Linear OA(898, 526, F8, 36) (dual of [526, 428, 37]-code) [i]
114Linear OA(899, 530, F8, 36) (dual of [530, 431, 37]-code) [i]
115Linear OA(898, 528, F8, 36) (dual of [528, 430, 37]-code) [i]
116Linear OA(8104, 537, F8, 37) (dual of [537, 433, 38]-code) [i]
117Linear OA(8107, 537, F8, 38) (dual of [537, 430, 39]-code) [i]
118Linear OA(8111, 529, F8, 41) (dual of [529, 418, 42]-code) [i]
119Linear OA(8113, 526, F8, 42) (dual of [526, 413, 43]-code) [i]
120Linear OA(8112, 524, F8, 42) (dual of [524, 412, 43]-code) [i]
121Linear OA(8116, 526, F8, 43) (dual of [526, 410, 44]-code) [i]
122Linear OA(8115, 524, F8, 43) (dual of [524, 409, 44]-code) [i]
123Linear OA(8117, 530, F8, 43) (dual of [530, 413, 44]-code) [i]
124Linear OA(8116, 528, F8, 43) (dual of [528, 412, 44]-code) [i]
125Linear OA(8120, 529, F8, 44) (dual of [529, 409, 45]-code) [i]
126Linear OA(8119, 526, F8, 44) (dual of [526, 407, 45]-code) [i]
127Linear OA(8120, 530, F8, 44) (dual of [530, 410, 45]-code) [i]
128Linear OA(8119, 528, F8, 44) (dual of [528, 409, 45]-code) [i]
129Linear OA(8125, 537, F8, 45) (dual of [537, 412, 46]-code) [i]
130Linear OA(8128, 537, F8, 46) (dual of [537, 409, 47]-code) [i]
131Linear OA(8132, 529, F8, 49) (dual of [529, 397, 50]-code) [i]
132Linear OA(8134, 526, F8, 50) (dual of [526, 392, 51]-code) [i]
133Linear OA(8133, 524, F8, 50) (dual of [524, 391, 51]-code) [i]
134Linear OA(8137, 526, F8, 51) (dual of [526, 389, 52]-code) [i]
135Linear OA(8136, 524, F8, 51) (dual of [524, 388, 52]-code) [i]
136Linear OA(8138, 530, F8, 51) (dual of [530, 392, 52]-code) [i]
137Linear OA(8137, 528, F8, 51) (dual of [528, 391, 52]-code) [i]
138Linear OA(8141, 529, F8, 52) (dual of [529, 388, 53]-code) [i]
139Linear OA(8140, 526, F8, 52) (dual of [526, 386, 53]-code) [i]
140Linear OA(8141, 530, F8, 52) (dual of [530, 389, 53]-code) [i]
141Linear OA(8140, 528, F8, 52) (dual of [528, 388, 53]-code) [i]
142Linear OA(8146, 537, F8, 53) (dual of [537, 391, 54]-code) [i]
143Linear OA(8149, 537, F8, 54) (dual of [537, 388, 55]-code) [i]
144Linear OA(8153, 529, F8, 57) (dual of [529, 376, 58]-code) [i]
145Linear OA(8155, 526, F8, 58) (dual of [526, 371, 59]-code) [i]
146Linear OA(8154, 524, F8, 58) (dual of [524, 370, 59]-code) [i]
147Linear OA(8158, 526, F8, 59) (dual of [526, 368, 60]-code) [i]
148Linear OA(8157, 524, F8, 59) (dual of [524, 367, 60]-code) [i]
149Linear OA(8159, 530, F8, 59) (dual of [530, 371, 60]-code) [i]
150Linear OA(8158, 528, F8, 59) (dual of [528, 370, 60]-code) [i]
151Linear OA(8162, 529, F8, 60) (dual of [529, 367, 61]-code) [i]
152Linear OA(8161, 526, F8, 60) (dual of [526, 365, 61]-code) [i]
153Linear OA(8162, 530, F8, 60) (dual of [530, 368, 61]-code) [i]
154Linear OA(8161, 528, F8, 60) (dual of [528, 367, 61]-code) [i]
155Linear OA(8167, 537, F8, 61) (dual of [537, 370, 62]-code) [i]
156Linear OA(8170, 537, F8, 62) (dual of [537, 367, 63]-code) [i]
157Linear OA(8128, 599, F8, 38) (dual of [599, 471, 39]-code) [i]
158Linear OA(8131, 599, F8, 39) (dual of [599, 468, 40]-code) [i]
159Linear OA(8116, 833, F8, 34) (dual of [833, 717, 35]-code) [i]
160Linear OA(8120, 833, F8, 35) (dual of [833, 713, 36]-code) [i]
161Linear OA(8132, 525, F8, 49) (dual of [525, 393, 50]-code) [i]Construction XX with a Chain of Cyclic Codes
162Linear OA(890, 525, F8, 33) (dual of [525, 435, 34]-code) [i]
163Linear OA(848, 525, F8, 17) (dual of [525, 477, 18]-code) [i]
164Linear OA(892, 830, F8, 27) (dual of [830, 738, 28]-code) [i]Construction X with Extended Narrow-Sense BCH Codes
165Linear OA(8157, 522, F8, 59) (dual of [522, 365, 60]-code) [i]
166Linear OA(8154, 522, F8, 58) (dual of [522, 368, 59]-code) [i]
167Linear OA(8151, 522, F8, 57) (dual of [522, 371, 58]-code) [i]
168Linear OA(8133, 522, F8, 50) (dual of [522, 389, 51]-code) [i]
169Linear OA(8115, 522, F8, 43) (dual of [522, 407, 44]-code) [i]
170Linear OA(8112, 522, F8, 42) (dual of [522, 410, 43]-code) [i]
171Linear OA(8109, 522, F8, 41) (dual of [522, 413, 42]-code) [i]
172Linear OA(891, 522, F8, 34) (dual of [522, 431, 35]-code) [i]
173Linear OA(873, 522, F8, 27) (dual of [522, 449, 28]-code) [i]
174Linear OA(870, 522, F8, 26) (dual of [522, 452, 27]-code) [i]
175Linear OA(867, 522, F8, 25) (dual of [522, 455, 26]-code) [i]
176Linear OA(849, 522, F8, 18) (dual of [522, 473, 19]-code) [i]
177Linear OA(831, 522, F8, 11) (dual of [522, 491, 12]-code) [i]
178Linear OA(828, 522, F8, 10) (dual of [522, 494, 11]-code) [i]
179Linear OA(825, 522, F8, 9) (dual of [522, 497, 10]-code) [i]
180Linear OA(849, 74, F8, 31) (dual of [74, 25, 32]-code) [i]
181Linear OA(842, 74, F8, 24) (dual of [74, 32, 25]-code) [i]
182Linear OA(838, 74, F8, 22) (dual of [74, 36, 23]-code) [i]
183Linear OA(831, 74, F8, 16) (dual of [74, 43, 17]-code) [i]
184Linear OA(829, 74, F8, 15) (dual of [74, 45, 16]-code) [i]
185Linear OA(827, 74, F8, 14) (dual of [74, 47, 15]-code) [i]
186Linear OA(825, 74, F8, 13) (dual of [74, 49, 14]-code) [i]
187Linear OA(8173, 523, F8, 66) (dual of [523, 350, 67]-code) [i]Construction XX with a Chain of Extended Narrow-Sense BCH Codes
188Linear OA(859, 75, F8, 41) (dual of [75, 16, 42]-code) [i]
189Linear OA(852, 75, F8, 33) (dual of [75, 23, 34]-code) [i]
190Linear OA(843, 75, F8, 25) (dual of [75, 32, 26]-code) [i]
191Linear OA(832, 75, F8, 17) (dual of [75, 43, 18]-code) [i]