Information on Result #628070
Linear OA(58, 52, F5, 4) (dual of [52, 44, 5]-code), using trace code based on linear OA(254, 26, F25, 4) (dual of [26, 22, 5]-code or 26-arc in PG(3,25)), using
- extended Reed–Solomon code RSe(22,25) [i]
- algebraic-geometric code AG(F, Q+9P) with degQ = 3 and degPÂ =Â 2 [i] based on function field F/F25 with g(F) = 0 and N(F) ≥ 26, using the rational function field F25(x) [i]
- algebraic-geometric code AG(F,7P) with degPÂ =Â 3 [i] based on function field F/F25 with g(F) = 0 and N(F) ≥ 26 (see above)
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:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | Linear OA(5137, 390666, F5, 20) (dual of [390666, 390529, 21]-code) | [i] | Construction X with Cyclic Codes | |
| 2 | Linear OA(5135, 78162, F5, 22) (dual of [78162, 78027, 23]-code) | [i] | ||
| 3 | Linear OA(5121, 78162, F5, 20) (dual of [78162, 78041, 21]-code) | [i] | ||
| 4 | Linear OA(5117, 15658, F5, 22) (dual of [15658, 15541, 23]-code) | [i] | ||
| 5 | Linear OA(5105, 15658, F5, 20) (dual of [15658, 15553, 21]-code) | [i] | ||
| 6 | Linear OA(5139, 3154, F5, 32) (dual of [3154, 3015, 33]-code) | [i] | ||
| 7 | Linear OA(5129, 3154, F5, 30) (dual of [3154, 3025, 31]-code) | [i] | ||
| 8 | Linear OA(599, 3154, F5, 22) (dual of [3154, 3055, 23]-code) | [i] | ||
| 9 | Linear OA(589, 3154, F5, 20) (dual of [3154, 3065, 21]-code) | [i] | ||
| 10 | Linear OA(5129, 3164, F5, 28) (dual of [3164, 3035, 29]-code) | [i] | ||
| 11 | Linear OA(5119, 3164, F5, 26) (dual of [3164, 3045, 27]-code) | [i] | ||
| 12 | Linear OA(5137, 658, F5, 38) (dual of [658, 521, 39]-code) | [i] | ||
| 13 | Linear OA(5129, 658, F5, 36) (dual of [658, 529, 37]-code) | [i] | ||
| 14 | Linear OA(597, 658, F5, 26) (dual of [658, 561, 27]-code) | [i] | ||
| 15 | Linear OA(5139, 661, F5, 38) (dual of [661, 522, 39]-code) | [i] | Construction XX with a Chain of Cyclic Codes | |
| 16 | Linear OA(5133, 663, F5, 36) (dual of [663, 530, 37]-code) | [i] | ||
| 17 | Linear OA(5144, 1953169, F5, 19) (dual of [1953169, 1953025, 20]-code) | [i] | Construction X with Extended Narrow-Sense BCH Codes | |
| 18 | Linear OA(5135, 1953169, F5, 18) (dual of [1953169, 1953034, 19]-code) | [i] | ||
| 19 | Linear OA(5126, 1953169, F5, 17) (dual of [1953169, 1953043, 18]-code) | [i] | ||
| 20 | Linear OA(5117, 1953169, F5, 16) (dual of [1953169, 1953052, 17]-code) | [i] | ||
| 21 | Linear OA(5108, 1953169, F5, 14) (dual of [1953169, 1953061, 15]-code) | [i] | ||
| 22 | Linear OA(599, 1953169, F5, 13) (dual of [1953169, 1953070, 14]-code) | [i] | ||
| 23 | Linear OA(590, 1953169, F5, 12) (dual of [1953169, 1953079, 13]-code) | [i] | ||
| 24 | Linear OA(5145, 390665, F5, 22) (dual of [390665, 390520, 23]-code) | [i] | ||
| 25 | Linear OA(5137, 390665, F5, 21) (dual of [390665, 390528, 22]-code) | [i] | ||
| 26 | Linear OA(5129, 390665, F5, 19) (dual of [390665, 390536, 20]-code) | [i] | ||
| 27 | Linear OA(5121, 390665, F5, 18) (dual of [390665, 390544, 19]-code) | [i] | ||
| 28 | Linear OA(5113, 390665, F5, 17) (dual of [390665, 390552, 18]-code) | [i] | ||
| 29 | Linear OA(5105, 390665, F5, 16) (dual of [390665, 390560, 17]-code) | [i] | ||
| 30 | Linear OA(597, 390665, F5, 14) (dual of [390665, 390568, 15]-code) | [i] | ||
| 31 | Linear OA(589, 390665, F5, 13) (dual of [390665, 390576, 14]-code) | [i] | ||
| 32 | Linear OA(581, 390665, F5, 12) (dual of [390665, 390584, 13]-code) | [i] | ||
| 33 | Linear OA(5149, 78161, F5, 26) (dual of [78161, 78012, 27]-code) | [i] | ||
| 34 | Linear OA(5142, 78161, F5, 24) (dual of [78161, 78019, 25]-code) | [i] | ||
| 35 | Linear OA(5135, 78161, F5, 23) (dual of [78161, 78026, 24]-code) | [i] | ||
| 36 | Linear OA(5128, 78161, F5, 22) (dual of [78161, 78033, 23]-code) | [i] | ||
| 37 | Linear OA(5121, 78161, F5, 21) (dual of [78161, 78040, 22]-code) | [i] | ||
| 38 | Linear OA(5114, 78161, F5, 19) (dual of [78161, 78047, 20]-code) | [i] | ||
| 39 | Linear OA(5107, 78161, F5, 18) (dual of [78161, 78054, 19]-code) | [i] | ||
| 40 | Linear OA(5100, 78161, F5, 17) (dual of [78161, 78061, 18]-code) | [i] | ||
| 41 | Linear OA(593, 78161, F5, 16) (dual of [78161, 78068, 17]-code) | [i] | ||
| 42 | Linear OA(586, 78161, F5, 14) (dual of [78161, 78075, 15]-code) | [i] | ||
| 43 | Linear OA(579, 78161, F5, 13) (dual of [78161, 78082, 14]-code) | [i] | ||
| 44 | Linear OA(572, 78161, F5, 12) (dual of [78161, 78089, 13]-code) | [i] | ||
| 45 | Linear OA(5147, 15657, F5, 29) (dual of [15657, 15510, 30]-code) | [i] | ||
| 46 | Linear OA(5141, 15657, F5, 28) (dual of [15657, 15516, 29]-code) | [i] | ||
| 47 | Linear OA(5135, 15657, F5, 27) (dual of [15657, 15522, 28]-code) | [i] | ||
| 48 | Linear OA(5129, 15657, F5, 26) (dual of [15657, 15528, 27]-code) | [i] | ||
| 49 | Linear OA(5123, 15657, F5, 24) (dual of [15657, 15534, 25]-code) | [i] | ||
| 50 | Linear OA(5117, 15657, F5, 23) (dual of [15657, 15540, 24]-code) | [i] | ||
| 51 | Linear OA(5111, 15657, F5, 22) (dual of [15657, 15546, 23]-code) | [i] | ||
| 52 | Linear OA(5105, 15657, F5, 21) (dual of [15657, 15552, 22]-code) | [i] | ||
| 53 | Linear OA(599, 15657, F5, 19) (dual of [15657, 15558, 20]-code) | [i] | ||
| 54 | Linear OA(593, 15657, F5, 18) (dual of [15657, 15564, 19]-code) | [i] | ||
| 55 | Linear OA(587, 15657, F5, 17) (dual of [15657, 15570, 18]-code) | [i] | ||
| 56 | Linear OA(581, 15657, F5, 16) (dual of [15657, 15576, 17]-code) | [i] | ||
| 57 | Linear OA(575, 15657, F5, 14) (dual of [15657, 15582, 15]-code) | [i] | ||
| 58 | Linear OA(569, 15657, F5, 13) (dual of [15657, 15588, 14]-code) | [i] | ||
| 59 | Linear OA(563, 15657, F5, 12) (dual of [15657, 15594, 13]-code) | [i] | ||
| 60 | Linear OA(5149, 3153, F5, 36) (dual of [3153, 3004, 37]-code) | [i] | ||
| 61 | Linear OA(5144, 3153, F5, 34) (dual of [3153, 3009, 35]-code) | [i] | ||
| 62 | Linear OA(5139, 3153, F5, 33) (dual of [3153, 3014, 34]-code) | [i] | ||
| 63 | Linear OA(5134, 3153, F5, 32) (dual of [3153, 3019, 33]-code) | [i] | ||
| 64 | Linear OA(5129, 3153, F5, 31) (dual of [3153, 3024, 32]-code) | [i] | ||
| 65 | Linear OA(5124, 3153, F5, 29) (dual of [3153, 3029, 30]-code) | [i] | ||
| 66 | Linear OA(5119, 3153, F5, 28) (dual of [3153, 3034, 29]-code) | [i] | ||
| 67 | Linear OA(5114, 3153, F5, 27) (dual of [3153, 3039, 28]-code) | [i] | ||
| 68 | Linear OA(5109, 3153, F5, 26) (dual of [3153, 3044, 27]-code) | [i] | ||
| 69 | Linear OA(5104, 3153, F5, 24) (dual of [3153, 3049, 25]-code) | [i] | ||
| 70 | Linear OA(599, 3153, F5, 23) (dual of [3153, 3054, 24]-code) | [i] | ||
| 71 | Linear OA(594, 3153, F5, 22) (dual of [3153, 3059, 23]-code) | [i] | ||
| 72 | Linear OA(589, 3153, F5, 21) (dual of [3153, 3064, 22]-code) | [i] | ||
| 73 | Linear OA(584, 3153, F5, 19) (dual of [3153, 3069, 20]-code) | [i] | ||
| 74 | Linear OA(579, 3153, F5, 18) (dual of [3153, 3074, 19]-code) | [i] | ||
| 75 | Linear OA(574, 3153, F5, 17) (dual of [3153, 3079, 18]-code) | [i] | ||
| 76 | Linear OA(569, 3153, F5, 16) (dual of [3153, 3084, 17]-code) | [i] | ||
| 77 | Linear OA(564, 3153, F5, 14) (dual of [3153, 3089, 15]-code) | [i] | ||
| 78 | Linear OA(559, 3153, F5, 13) (dual of [3153, 3094, 14]-code) | [i] | ||
| 79 | Linear OA(5148, 15659, F5, 29) (dual of [15659, 15511, 30]-code) | [i] | Construction XX with a Chain of Extended Narrow-Sense BCH Codes | |
| 80 | Linear OA(5142, 15659, F5, 28) (dual of [15659, 15517, 29]-code) | [i] | ||
| 81 | Linear OA(5136, 15659, F5, 27) (dual of [15659, 15523, 28]-code) | [i] | ||
| 82 | Linear OA(5131, 15660, F5, 26) (dual of [15660, 15529, 27]-code) | [i] | ||
| 83 | Linear OA(5124, 15659, F5, 24) (dual of [15659, 15535, 25]-code) | [i] | ||
| 84 | Linear OA(5118, 15659, F5, 23) (dual of [15659, 15541, 24]-code) | [i] | ||
| 85 | Linear OA(5112, 15659, F5, 22) (dual of [15659, 15547, 23]-code) | [i] | ||
| 86 | Linear OA(5100, 15659, F5, 19) (dual of [15659, 15559, 20]-code) | [i] | ||
| 87 | Linear OA(594, 15659, F5, 18) (dual of [15659, 15565, 19]-code) | [i] | ||
| 88 | Linear OA(588, 15659, F5, 17) (dual of [15659, 15571, 18]-code) | [i] | ||
| 89 | Linear OA(583, 15660, F5, 16) (dual of [15660, 15577, 17]-code) | [i] | ||
| 90 | Linear OA(576, 15659, F5, 14) (dual of [15659, 15583, 15]-code) | [i] | ||
| 91 | Linear OA(570, 15659, F5, 13) (dual of [15659, 15589, 14]-code) | [i] | ||
| 92 | Linear OA(5145, 3155, F5, 34) (dual of [3155, 3010, 35]-code) | [i] | ||
| 93 | Linear OA(5140, 3155, F5, 33) (dual of [3155, 3015, 34]-code) | [i] | ||
| 94 | Linear OA(5135, 3155, F5, 32) (dual of [3155, 3020, 33]-code) | [i] | ||
| 95 | Linear OA(5132, 3158, F5, 31) (dual of [3158, 3026, 32]-code) | [i] | ||
| 96 | Linear OA(5125, 3155, F5, 29) (dual of [3155, 3030, 30]-code) | [i] | ||
| 97 | Linear OA(5120, 3155, F5, 28) (dual of [3155, 3035, 29]-code) | [i] | ||
| 98 | Linear OA(5115, 3155, F5, 27) (dual of [3155, 3040, 28]-code) | [i] | ||
| 99 | Linear OA(5112, 3158, F5, 26) (dual of [3158, 3046, 27]-code) | [i] | ||
| 100 | Linear OA(5111, 3156, F5, 26) (dual of [3156, 3045, 27]-code) | [i] | ||
| 101 | Linear OA(5105, 3155, F5, 24) (dual of [3155, 3050, 25]-code) | [i] | ||
| 102 | Linear OA(5100, 3155, F5, 23) (dual of [3155, 3055, 24]-code) | [i] | ||
| 103 | Linear OA(595, 3155, F5, 22) (dual of [3155, 3060, 23]-code) | [i] | ||
| 104 | Linear OA(592, 3158, F5, 21) (dual of [3158, 3066, 22]-code) | [i] | ||
| 105 | Linear OA(585, 3155, F5, 19) (dual of [3155, 3070, 20]-code) | [i] | ||
| 106 | Linear OA(580, 3155, F5, 18) (dual of [3155, 3075, 19]-code) | [i] | ||
| 107 | Linear OA(575, 3155, F5, 17) (dual of [3155, 3080, 18]-code) | [i] | ||
| 108 | Linear OA(571, 3156, F5, 16) (dual of [3156, 3085, 17]-code) | [i] | ||
| 109 | Linear OA(565, 3155, F5, 14) (dual of [3155, 3090, 15]-code) | [i] | ||