Information on Result #608007

Linear OA(52, 6, F5, 2) (dual of [6, 4, 3]-code or 6-arc in PG(1,5)), using Hamming code H(2,5)

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

Depending Results

The following results depend on this result:

ResultThis
result
only		Method
1Linear OA(516, 1208, F5, 5) (dual of [1208, 1192, 6]-code) [i](u, u+v)-Construction
2Linear OA(530, 78130, F5, 5) (dual of [78130, 78100, 6]-code) [i]
3Linear OA(538, 1953130, F5, 5) (dual of [1953130, 1953092, 6]-code) [i]
4Linear OA(524, 78131, F5, 4) (dual of [78131, 78107, 5]-code) [i]
5Linear OA(530, 1953131, F5, 4) (dual of [1953131, 1953101, 5]-code) [i]
6Linear OA(521, 30, F5, 14) (dual of [30, 9, 15]-code) [i]Generalized (u, u+v)-Construction
7Linear OA(524, 34, F5, 14) (dual of [34, 10, 15]-code) [i]
8Linear OA(525, 36, F5, 14) (dual of [36, 11, 15]-code) [i]
9Linear OA(513, 30, F5, 7) (dual of [30, 17, 8]-code) [i]
10Linear OA(528, 32, F5, 22) (dual of [32, 4, 23]-code) [i]Juxtaposition
11Linear OA(517, 1214, F5, 5) (dual of [1214, 1197, 6]-code) [i](u, u−v, u+v+w)-Construction
12Linear OA(531, 78136, F5, 5) (dual of [78136, 78105, 6]-code) [i]
13Linear OA(539, 1953136, F5, 5) (dual of [1953136, 1953097, 6]-code) [i]
14Linear OA(5147, 1953132, F5, 20) (dual of [1953132, 1952985, 21]-code) [i]Construction X with Cyclic Codes
15Linear OA(575, 1953132, F5, 10) (dual of [1953132, 1953057, 11]-code) [i]
16Linear OA(5131, 390632, F5, 20) (dual of [390632, 390501, 21]-code) [i]
17Linear OA(567, 390632, F5, 10) (dual of [390632, 390565, 11]-code) [i]
18Linear OA(5115, 78132, F5, 20) (dual of [78132, 78017, 21]-code) [i]
19Linear OA(559, 78132, F5, 10) (dual of [78132, 78073, 11]-code) [i]
20Linear OA(5147, 15632, F5, 30) (dual of [15632, 15485, 31]-code) [i]
21Linear OA(599, 15632, F5, 20) (dual of [15632, 15533, 21]-code) [i]
22Linear OA(551, 15632, F5, 10) (dual of [15632, 15581, 11]-code) [i]
23Linear OA(5123, 3132, F5, 30) (dual of [3132, 3009, 31]-code) [i]
24Linear OA(583, 3132, F5, 20) (dual of [3132, 3049, 21]-code) [i]
25Linear OA(543, 3132, F5, 10) (dual of [3132, 3089, 11]-code) [i]
26Linear OA(5131, 632, F5, 40) (dual of [632, 501, 41]-code) [i]
27Linear OA(599, 632, F5, 30) (dual of [632, 533, 31]-code) [i]
28Linear OA(567, 632, F5, 20) (dual of [632, 565, 21]-code) [i]
29Linear OA(535, 632, F5, 10) (dual of [632, 597, 11]-code) [i]
30Linear OA(5123, 319, F5, 40) (dual of [319, 196, 41]-code) [i]
31Linear OA(591, 319, F5, 30) (dual of [319, 228, 31]-code) [i]
32Linear OA(5143, 162, F5, 86) (dual of [162, 19, 87]-code) [i]
33Linear OA(527, 132, F5, 10) (dual of [132, 105, 11]-code) [i]
34Linear OA(522, 30, F5, 15) (dual of [30, 8, 16]-code) [i]
35Linear OA(524, 37, F5, 13) (dual of [37, 13, 14]-code) [i]
36Linear OA(530, 37, F5, 21) (dual of [37, 7, 22]-code) [i]
37Linear OA(536, 68, F5, 18) (dual of [68, 32, 19]-code) [i]
38Linear OA(5147, 787, F5, 39) (dual of [787, 640, 40]-code) [i]
39Linear OA(523, 31, F5, 16) (dual of [31, 8, 17]-code) [i]Construction XX with Cyclic Codes
40Linear OA(525, 35, F5, 15) (dual of [35, 10, 16]-code) [i]
41Linear OA(541, 76, F5, 18) (dual of [76, 35, 19]-code) [i]
42Linear OA(539, 71, F5, 19) (dual of [71, 32, 20]-code) [i]
43Linear OA(542, 71, F5, 20) (dual of [71, 29, 21]-code) [i]
44Linear OA(545, 77, F5, 21) (dual of [77, 32, 22]-code) [i]
45Linear OA(543, 75, F5, 20) (dual of [75, 32, 21]-code) [i]
46Linear OA(543, 72, F5, 21) (dual of [72, 29, 22]-code) [i]
47Linear OA(551, 83, F5, 23) (dual of [83, 32, 24]-code) [i]
48Linear OA(549, 81, F5, 22) (dual of [81, 32, 23]-code) [i]
49Linear OA(559, 72, F5, 36) (dual of [72, 13, 37]-code) [i]
50Linear OA(518, 133, F5, 7) (dual of [133, 115, 8]-code) [i]
51Linear OA(519, 135, F5, 7) (dual of [135, 116, 8]-code) [i]
52Linear OA(522, 137, F5, 8) (dual of [137, 115, 9]-code) [i]
53Linear OA(531, 135, F5, 12) (dual of [135, 104, 13]-code) [i]
54Linear OA(530, 133, F5, 12) (dual of [133, 103, 13]-code) [i]
55Linear OA(534, 137, F5, 13) (dual of [137, 103, 14]-code) [i]
56Linear OA(543, 135, F5, 17) (dual of [135, 92, 18]-code) [i]
57Linear OA(542, 133, F5, 17) (dual of [133, 91, 18]-code) [i]
58Linear OA(546, 137, F5, 18) (dual of [137, 91, 19]-code) [i]
59Linear OA(588, 158, F5, 36) (dual of [158, 70, 37]-code) [i]
60Linear OA(592, 159, F5, 38) (dual of [159, 67, 39]-code) [i]
61Linear OA(586, 323, F5, 28) (dual of [323, 237, 29]-code) [i]
62Linear OA(590, 327, F5, 29) (dual of [327, 237, 30]-code) [i]
63Linear OA(588, 323, F5, 29) (dual of [323, 235, 30]-code) [i]
64Linear OA(587, 320, F5, 29) (dual of [320, 233, 30]-code) [i]
65Linear OA(591, 322, F5, 30) (dual of [322, 231, 31]-code) [i]
66Linear OA(594, 327, F5, 31) (dual of [327, 233, 32]-code) [i]
67Linear OA(592, 323, F5, 31) (dual of [323, 231, 32]-code) [i]
68Linear OA(595, 322, F5, 32) (dual of [322, 227, 33]-code) [i]
69Linear OA(5100, 327, F5, 33) (dual of [327, 227, 34]-code) [i]
70Linear OA(5111, 322, F5, 37) (dual of [322, 211, 38]-code) [i]
71Linear OA(5116, 327, F5, 38) (dual of [327, 211, 39]-code) [i]
72Linear OA(5121, 320, F5, 40) (dual of [320, 199, 41]-code) [i]
73Linear OA(5141, 322, F5, 47) (dual of [322, 181, 48]-code) [i]
74Linear OA(523, 634, F5, 7) (dual of [634, 611, 8]-code) [i]
75Linear OA(528, 639, F5, 8) (dual of [639, 611, 9]-code) [i]
76Linear OA(539, 634, F5, 12) (dual of [634, 595, 13]-code) [i]
77Linear OA(555, 634, F5, 17) (dual of [634, 579, 18]-code) [i]
78Linear OA(571, 634, F5, 22) (dual of [634, 563, 23]-code) [i]
79Linear OA(590, 636, F5, 28) (dual of [636, 546, 29]-code) [i]
80Linear OA(589, 634, F5, 28) (dual of [634, 545, 29]-code) [i]
81Linear OA(594, 639, F5, 29) (dual of [639, 545, 30]-code) [i]
82Linear OA(5101, 634, F5, 32) (dual of [634, 533, 33]-code) [i]
83Linear OA(5117, 634, F5, 37) (dual of [634, 517, 38]-code) [i]
84Linear OA(5133, 634, F5, 42) (dual of [634, 501, 43]-code) [i]
85Linear OA(5149, 634, F5, 47) (dual of [634, 485, 48]-code) [i]
86Linear OA(5123, 656, F5, 34) (dual of [656, 533, 35]-code) [i]Construction XX with a Chain of Cyclic Codes
87Linear OA(591, 656, F5, 24) (dual of [656, 565, 25]-code) [i]
88Linear OA(523, 39, F5, 12) (dual of [39, 16, 13]-code) [i]
89Linear OA(585, 631, F5, 27) (dual of [631, 546, 28]-code) [i]Construction X with Extended Narrow-Sense BCH Codes
90Linear OA(5121, 319, F5, 40) (dual of [319, 198, 41]-code) [i]
91Linear OA(5123, 131, F5, 96) (dual of [131, 8, 97]-code) [i]
92Linear OA(5107, 131, F5, 66) (dual of [131, 24, 67]-code) [i]
93Linear OA(591, 131, F5, 46) (dual of [131, 40, 47]-code) [i]
94Linear OA(582, 131, F5, 41) (dual of [131, 49, 42]-code) [i]
95Linear OA(573, 131, F5, 36) (dual of [131, 58, 37]-code) [i]
96Linear OA(539, 131, F5, 16) (dual of [131, 92, 17]-code) [i]
97Linear OA(530, 131, F5, 12) (dual of [131, 101, 13]-code) [i]
98Linear OA(527, 131, F5, 11) (dual of [131, 104, 12]-code) [i]
99Linear OA(518, 131, F5, 7) (dual of [131, 113, 8]-code) [i]
100Linear OA(515, 131, F5, 6) (dual of [131, 116, 7]-code) [i]
101Linear OA(555, 69, F5, 34) (dual of [69, 14, 35]-code) [i]
102Linear OA(542, 69, F5, 20) (dual of [69, 27, 21]-code) [i]
103Linear OA(539, 69, F5, 19) (dual of [69, 30, 20]-code) [i]
104Linear OA(533, 69, F5, 14) (dual of [69, 36, 15]-code) [i]
105Linear OA(511, 31, F5, 6) (dual of [31, 20, 7]-code) [i]
106Linear OA(5124, 132, F5, 97) (dual of [132, 8, 98]-code) [i]Construction XX with a Chain of Extended Narrow-Sense BCH Codes
107Linear OA(5114, 132, F5, 72) (dual of [132, 18, 73]-code) [i]
108Linear OA(5108, 132, F5, 67) (dual of [132, 24, 68]-code) [i]
109Linear OA(5101, 132, F5, 52) (dual of [132, 31, 53]-code) [i]
110Linear OA(592, 132, F5, 47) (dual of [132, 40, 48]-code) [i]
111Linear OA(5101, 156, F5, 44) (dual of [156, 55, 45]-code) [i]
112Linear OA(583, 132, F5, 42) (dual of [132, 49, 43]-code) [i]
113Linear OA(574, 132, F5, 37) (dual of [132, 58, 38]-code) [i]
114Linear OA(581, 158, F5, 32) (dual of [158, 77, 33]-code) [i]
115Linear OA(534, 70, F5, 15) (dual of [70, 36, 16]-code) [i]
116Linear OA(513, 32, F5, 7) (dual of [32, 19, 8]-code) [i]