Information on Result #604899

Linear OA(51, 2, F5, 1) (dual of [2, 1, 2]-code), using dual of repetition code with length 2

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(5104, 167, F5, 44) (dual of [167, 63, 45]-code) [i]Construction XX with Cyclic Codes
2Linear OA(5102, 166, F5, 43) (dual of [166, 64, 44]-code) [i]
3Linear OA(599, 162, F5, 43) (dual of [162, 63, 44]-code) [i]
4Linear OA(596, 160, F5, 42) (dual of [160, 64, 43]-code) [i]
5Linear OA(596, 160, F5, 42) (dual of [160, 64, 43]-code) [i]
6Linear OA(523, 36, F5, 13) (dual of [36, 13, 14]-code) [i]
7Linear OA(522, 38, F5, 12) (dual of [38, 16, 13]-code) [i]
8Linear OA(5148, 638, F5, 45) (dual of [638, 490, 46]-code) [i]Construction XX with a Chain of Cyclic Codes
9Linear OA(5148, 654, F5, 43) (dual of [654, 506, 44]-code) [i]
10Linear OA(5146, 652, F5, 42) (dual of [652, 506, 43]-code) [i]
11Linear OA(5135, 641, F5, 41) (dual of [641, 506, 42]-code) [i]
12Linear OA(5132, 638, F5, 39) (dual of [638, 506, 40]-code) [i]
13Linear OA(5140, 654, F5, 41) (dual of [654, 514, 42]-code) [i]
14Linear OA(5138, 652, F5, 40) (dual of [652, 514, 41]-code) [i]
15Linear OA(5135, 649, F5, 39) (dual of [649, 514, 40]-code) [i]
16Linear OA(5139, 661, F5, 38) (dual of [661, 522, 39]-code) [i]
17Linear OA(5124, 638, F5, 37) (dual of [638, 514, 38]-code) [i]
18Linear OA(5127, 649, F5, 37) (dual of [649, 522, 38]-code) [i]
19Linear OA(5116, 638, F5, 35) (dual of [638, 522, 36]-code) [i]
20Linear OA(5116, 654, F5, 33) (dual of [654, 538, 34]-code) [i]
21Linear OA(5114, 652, F5, 32) (dual of [652, 538, 33]-code) [i]
22Linear OA(5103, 641, F5, 31) (dual of [641, 538, 32]-code) [i]
23Linear OA(5100, 638, F5, 29) (dual of [638, 538, 30]-code) [i]
24Linear OA(5108, 654, F5, 31) (dual of [654, 546, 32]-code) [i]
25Linear OA(5106, 652, F5, 30) (dual of [652, 546, 31]-code) [i]
26Linear OA(5103, 649, F5, 29) (dual of [649, 546, 30]-code) [i]
27Linear OA(592, 638, F5, 27) (dual of [638, 546, 28]-code) [i]
28Linear OA(595, 649, F5, 27) (dual of [649, 554, 28]-code) [i]
29Linear OA(584, 638, F5, 25) (dual of [638, 554, 26]-code) [i]
30Linear OA(584, 654, F5, 23) (dual of [654, 570, 24]-code) [i]
31Linear OA(582, 652, F5, 22) (dual of [652, 570, 23]-code) [i]
32Linear OA(571, 641, F5, 21) (dual of [641, 570, 22]-code) [i]
33Linear OA(568, 638, F5, 19) (dual of [638, 570, 20]-code) [i]
34Linear OA(576, 654, F5, 21) (dual of [654, 578, 22]-code) [i]
35Linear OA(574, 652, F5, 20) (dual of [652, 578, 21]-code) [i]
36Linear OA(571, 649, F5, 19) (dual of [649, 578, 20]-code) [i]
37Linear OA(560, 638, F5, 17) (dual of [638, 578, 18]-code) [i]
38Linear OA(563, 649, F5, 17) (dual of [649, 586, 18]-code) [i]
39Linear OA(552, 638, F5, 15) (dual of [638, 586, 16]-code) [i]
40Linear OA(539, 641, F5, 11) (dual of [641, 602, 12]-code) [i]
41Linear OA(5108, 325, F5, 35) (dual of [325, 217, 36]-code) [i]
42Linear OA(5105, 168, F5, 44) (dual of [168, 63, 45]-code) [i]
43Linear OA(5100, 163, F5, 43) (dual of [163, 63, 44]-code) [i]
44Linear OA(5123, 145, F5, 73) (dual of [145, 22, 74]-code) [i]
45Linear OA(5120, 142, F5, 71) (dual of [142, 22, 72]-code) [i]
46Linear OA(5117, 139, F5, 69) (dual of [139, 22, 70]-code) [i]
47Linear OA(5114, 136, F5, 67) (dual of [136, 22, 68]-code) [i]
48Linear OA(531, 139, F5, 11) (dual of [139, 108, 12]-code) [i]
49Linear OA(523, 39, F5, 12) (dual of [39, 16, 13]-code) [i]
50Linear OA(5139, 390636, F5, 22) (dual of [390636, 390497, 23]-code) [i]Construction XX with a Chain of Extended Narrow-Sense BCH Codes
51Linear OA(5126, 390655, F5, 19) (dual of [390655, 390529, 20]-code) [i]
52Linear OA(5116, 390645, F5, 18) (dual of [390645, 390529, 19]-code) [i]
53Linear OA(5107, 390636, F5, 17) (dual of [390636, 390529, 18]-code) [i]
54Linear OA(594, 390655, F5, 14) (dual of [390655, 390561, 15]-code) [i]
55Linear OA(575, 390636, F5, 12) (dual of [390636, 390561, 13]-code) [i]
56Linear OA(562, 390655, F5, 9) (dual of [390655, 390593, 10]-code) [i]
57Linear OA(5150, 78135, F5, 27) (dual of [78135, 77985, 28]-code) [i]
58Linear OA(5139, 78152, F5, 24) (dual of [78152, 78013, 25]-code) [i]
59Linear OA(5122, 78135, F5, 22) (dual of [78135, 78013, 23]-code) [i]
60Linear OA(5111, 78152, F5, 19) (dual of [78152, 78041, 20]-code) [i]
61Linear OA(5102, 78143, F5, 18) (dual of [78143, 78041, 19]-code) [i]
62Linear OA(594, 78135, F5, 17) (dual of [78135, 78041, 18]-code) [i]
63Linear OA(583, 78152, F5, 14) (dual of [78152, 78069, 15]-code) [i]
64Linear OA(566, 78135, F5, 12) (dual of [78135, 78069, 13]-code) [i]
65Linear OA(555, 78152, F5, 9) (dual of [78152, 78097, 10]-code) [i]
66Linear OA(5144, 15649, F5, 29) (dual of [15649, 15505, 30]-code) [i]
67Linear OA(5136, 15641, F5, 28) (dual of [15641, 15505, 29]-code) [i]
68Linear OA(5129, 15634, F5, 27) (dual of [15634, 15505, 28]-code) [i]
69Linear OA(5131, 15660, F5, 26) (dual of [15660, 15529, 27]-code) [i]
70Linear OA(5120, 15649, F5, 24) (dual of [15649, 15529, 25]-code) [i]
71Linear OA(5105, 15634, F5, 22) (dual of [15634, 15529, 23]-code) [i]
72Linear OA(5104, 15657, F5, 20) (dual of [15657, 15553, 21]-code) [i]
73Linear OA(596, 15649, F5, 19) (dual of [15649, 15553, 20]-code) [i]
74Linear OA(588, 15641, F5, 18) (dual of [15641, 15553, 19]-code) [i]
75Linear OA(581, 15634, F5, 17) (dual of [15634, 15553, 18]-code) [i]
76Linear OA(583, 15660, F5, 16) (dual of [15660, 15577, 17]-code) [i]
77Linear OA(572, 15649, F5, 14) (dual of [15649, 15577, 15]-code) [i]
78Linear OA(557, 15634, F5, 12) (dual of [15634, 15577, 13]-code) [i]
79Linear OA(548, 15649, F5, 9) (dual of [15649, 15601, 10]-code) [i]
80Linear OA(533, 15634, F5, 7) (dual of [15634, 15601, 8]-code) [i]
81Linear OA(5148, 3133, F5, 37) (dual of [3133, 2985, 38]-code) [i]
82Linear OA(5141, 3146, F5, 34) (dual of [3146, 3005, 35]-code) [i]
83Linear OA(5128, 3133, F5, 32) (dual of [3133, 3005, 33]-code) [i]
84Linear OA(5127, 3152, F5, 30) (dual of [3152, 3025, 31]-code) [i]
85Linear OA(5121, 3146, F5, 29) (dual of [3146, 3025, 30]-code) [i]
86Linear OA(5114, 3139, F5, 28) (dual of [3139, 3025, 29]-code) [i]
87Linear OA(5108, 3133, F5, 27) (dual of [3133, 3025, 28]-code) [i]
88Linear OA(5111, 3156, F5, 26) (dual of [3156, 3045, 27]-code) [i]
89Linear OA(5101, 3146, F5, 24) (dual of [3146, 3045, 25]-code) [i]
90Linear OA(588, 3133, F5, 22) (dual of [3133, 3045, 23]-code) [i]
91Linear OA(587, 3152, F5, 20) (dual of [3152, 3065, 21]-code) [i]
92Linear OA(581, 3146, F5, 19) (dual of [3146, 3065, 20]-code) [i]
93Linear OA(574, 3139, F5, 18) (dual of [3139, 3065, 19]-code) [i]
94Linear OA(568, 3133, F5, 17) (dual of [3133, 3065, 18]-code) [i]
95Linear OA(571, 3156, F5, 16) (dual of [3156, 3085, 17]-code) [i]
96Linear OA(561, 3146, F5, 14) (dual of [3146, 3085, 15]-code) [i]
97Linear OA(548, 3133, F5, 12) (dual of [3133, 3085, 13]-code) [i]
98Linear OA(541, 3146, F5, 9) (dual of [3146, 3105, 10]-code) [i]
99Linear OA(528, 3133, F5, 7) (dual of [3133, 3105, 8]-code) [i]
100Linear OA(5149, 632, F5, 47) (dual of [632, 483, 48]-code) [i]
101Linear OA(5149, 648, F5, 45) (dual of [648, 499, 46]-code) [i]
102Linear OA(5144, 643, F5, 44) (dual of [643, 499, 45]-code) [i]
103Linear OA(5138, 637, F5, 43) (dual of [637, 499, 44]-code) [i]
104Linear OA(5133, 632, F5, 42) (dual of [632, 499, 43]-code) [i]
105Linear OA(5143, 658, F5, 42) (dual of [658, 515, 43]-code) [i]
106Linear OA(5136, 651, F5, 41) (dual of [651, 515, 42]-code) [i]
107Linear OA(5133, 648, F5, 40) (dual of [648, 515, 41]-code) [i]
108Linear OA(5128, 643, F5, 39) (dual of [643, 515, 40]-code) [i]
109Linear OA(5122, 637, F5, 38) (dual of [637, 515, 39]-code) [i]
110Linear OA(5117, 632, F5, 37) (dual of [632, 515, 38]-code) [i]
111Linear OA(5127, 658, F5, 37) (dual of [658, 531, 38]-code) [i]
112Linear OA(5120, 651, F5, 36) (dual of [651, 531, 37]-code) [i]
113Linear OA(5117, 648, F5, 35) (dual of [648, 531, 36]-code) [i]
114Linear OA(5112, 643, F5, 34) (dual of [643, 531, 35]-code) [i]
115Linear OA(5106, 637, F5, 33) (dual of [637, 531, 34]-code) [i]
116Linear OA(5117, 662, F5, 33) (dual of [662, 545, 34]-code) [i]
117Linear OA(5101, 632, F5, 32) (dual of [632, 531, 33]-code) [i]
118Linear OA(5101, 646, F5, 30) (dual of [646, 545, 31]-code) [i]
119Linear OA(596, 641, F5, 29) (dual of [641, 545, 30]-code) [i]
120Linear OA(590, 635, F5, 28) (dual of [635, 545, 29]-code) [i]
121Linear OA(5101, 662, F5, 28) (dual of [662, 561, 29]-code) [i]
122Linear OA(595, 656, F5, 27) (dual of [656, 561, 28]-code) [i]
123Linear OA(592, 653, F5, 26) (dual of [653, 561, 27]-code) [i]
124Linear OA(590, 651, F5, 26) (dual of [651, 561, 27]-code) [i]
125Linear OA(582, 643, F5, 24) (dual of [643, 561, 25]-code) [i]
126Linear OA(571, 632, F5, 22) (dual of [632, 561, 23]-code) [i]
127Linear OA(581, 658, F5, 22) (dual of [658, 577, 23]-code) [i]
128Linear OA(571, 648, F5, 20) (dual of [648, 577, 21]-code) [i]
129Linear OA(566, 643, F5, 19) (dual of [643, 577, 20]-code) [i]
130Linear OA(560, 637, F5, 18) (dual of [637, 577, 19]-code) [i]
131Linear OA(555, 632, F5, 17) (dual of [632, 577, 18]-code) [i]
132Linear OA(558, 651, F5, 16) (dual of [651, 593, 17]-code) [i]
133Linear OA(550, 643, F5, 14) (dual of [643, 593, 15]-code) [i]
134Linear OA(539, 632, F5, 12) (dual of [632, 593, 13]-code) [i]
135Linear OA(523, 632, F5, 7) (dual of [632, 609, 8]-code) [i]
136Linear OA(5141, 320, F5, 47) (dual of [320, 179, 48]-code) [i]
137Linear OA(5136, 331, F5, 44) (dual of [331, 195, 45]-code) [i]
138Linear OA(5130, 325, F5, 43) (dual of [325, 195, 44]-code) [i]
139Linear OA(5133, 330, F5, 43) (dual of [330, 197, 44]-code) [i]
140Linear OA(5125, 320, F5, 42) (dual of [320, 195, 43]-code) [i]
141Linear OA(5128, 325, F5, 42) (dual of [325, 197, 43]-code) [i]
142Linear OA(5125, 330, F5, 40) (dual of [330, 205, 41]-code) [i]
143Linear OA(5122, 327, F5, 39) (dual of [327, 205, 40]-code) [i]
144Linear OA(5100, 164, F5, 42) (dual of [164, 64, 43]-code) [i]
145Linear OA(578, 155, F5, 32) (dual of [155, 77, 33]-code) [i]
146Linear OA(573, 150, F5, 29) (dual of [150, 77, 30]-code) [i]
147Linear OA(545, 146, F5, 16) (dual of [146, 101, 17]-code) [i]
148Linear OA(539, 140, F5, 14) (dual of [140, 101, 15]-code) [i]
149Linear OA(527, 140, F5, 9) (dual of [140, 113, 10]-code) [i]
150Linear OA(522, 135, F5, 8) (dual of [135, 113, 9]-code) [i]
151Linear OA(543, 70, F5, 21) (dual of [70, 27, 22]-code) [i]
152Linear OA(515, 32, F5, 8) (dual of [32, 17, 9]-code) [i]
153Linear OA(5130, 15659, F5, 26) (dual of [15659, 15529, 27]-code) [i]
154Linear OA(582, 15659, F5, 16) (dual of [15659, 15577, 17]-code) [i]
155Linear OA(5149, 3154, F5, 36) (dual of [3154, 3005, 37]-code) [i]
156Linear OA(5109, 3154, F5, 26) (dual of [3154, 3045, 27]-code) [i]
157Linear OA(569, 3154, F5, 16) (dual of [3154, 3085, 17]-code) [i]
158Linear OA(5103, 648, F5, 31) (dual of [648, 545, 32]-code) [i]
159Linear OA(592, 653, F5, 27) (dual of [653, 561, 28]-code) [i]