Information on Result #658956
Linear OA(57, 26, F5, 4) (dual of [26, 19, 5]-code), using base reduction for projective spaces (embedding PG(3,25) in PG(6,5)) 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(5136, 390652, F5, 20) (dual of [390652, 390516, 21]-code) | [i] | Construction X with Cyclic Codes | |
| 2 | Linear OA(5134, 78152, F5, 22) (dual of [78152, 78018, 23]-code) | [i] | ||
| 3 | Linear OA(5120, 78152, F5, 20) (dual of [78152, 78032, 21]-code) | [i] | ||
| 4 | Linear OA(5116, 15652, F5, 22) (dual of [15652, 15536, 23]-code) | [i] | ||
| 5 | Linear OA(5104, 15652, F5, 20) (dual of [15652, 15548, 21]-code) | [i] | ||
| 6 | Linear OA(5138, 3152, F5, 32) (dual of [3152, 3014, 33]-code) | [i] | ||
| 7 | Linear OA(5128, 3152, F5, 30) (dual of [3152, 3024, 31]-code) | [i] | ||
| 8 | Linear OA(598, 3152, F5, 22) (dual of [3152, 3054, 23]-code) | [i] | ||
| 9 | Linear OA(588, 3152, F5, 20) (dual of [3152, 3064, 21]-code) | [i] | ||
| 10 | Linear OA(5136, 652, F5, 38) (dual of [652, 516, 39]-code) | [i] | ||
| 11 | Linear OA(5128, 652, F5, 36) (dual of [652, 524, 37]-code) | [i] | ||
| 12 | Linear OA(596, 652, F5, 26) (dual of [652, 556, 27]-code) | [i] | ||
| 13 | Linear OA(5148, 656, F5, 42) (dual of [656, 508, 43]-code) | [i] | Construction XX with a Chain of Cyclic Codes | |
| 14 | Linear OA(5140, 656, F5, 40) (dual of [656, 516, 41]-code) | [i] | ||
| 15 | Linear OA(5116, 656, F5, 32) (dual of [656, 540, 33]-code) | [i] | ||
| 16 | Linear OA(5108, 656, F5, 30) (dual of [656, 548, 31]-code) | [i] | ||
| 17 | Linear OA(584, 656, F5, 22) (dual of [656, 572, 23]-code) | [i] | ||
| 18 | Linear OA(576, 656, F5, 20) (dual of [656, 580, 21]-code) | [i] | ||
| 19 | Linear OA(5146, 15651, F5, 29) (dual of [15651, 15505, 30]-code) | [i] | Construction X with Extended Narrow-Sense BCH Codes | |
| 20 | Linear OA(5140, 15651, F5, 28) (dual of [15651, 15511, 29]-code) | [i] | ||
| 21 | Linear OA(5134, 15651, F5, 27) (dual of [15651, 15517, 28]-code) | [i] | ||
| 22 | Linear OA(5128, 15651, F5, 26) (dual of [15651, 15523, 27]-code) | [i] | ||
| 23 | Linear OA(5122, 15651, F5, 24) (dual of [15651, 15529, 25]-code) | [i] | ||
| 24 | Linear OA(5116, 15651, F5, 23) (dual of [15651, 15535, 24]-code) | [i] | ||
| 25 | Linear OA(5110, 15651, F5, 22) (dual of [15651, 15541, 23]-code) | [i] | ||
| 26 | Linear OA(5104, 15651, F5, 21) (dual of [15651, 15547, 22]-code) | [i] | ||
| 27 | Linear OA(598, 15651, F5, 19) (dual of [15651, 15553, 20]-code) | [i] | ||
| 28 | Linear OA(592, 15651, F5, 18) (dual of [15651, 15559, 19]-code) | [i] | ||
| 29 | Linear OA(586, 15651, F5, 17) (dual of [15651, 15565, 18]-code) | [i] | ||
| 30 | Linear OA(580, 15651, F5, 16) (dual of [15651, 15571, 17]-code) | [i] | ||
| 31 | Linear OA(574, 15651, F5, 14) (dual of [15651, 15577, 15]-code) | [i] | ||
| 32 | Linear OA(568, 15651, F5, 13) (dual of [15651, 15583, 14]-code) | [i] | ||
| 33 | Linear OA(562, 15651, F5, 12) (dual of [15651, 15589, 13]-code) | [i] | ||
| 34 | Linear OA(556, 15651, F5, 11) (dual of [15651, 15595, 12]-code) | [i] | ||
| 35 | Linear OA(5148, 3151, F5, 36) (dual of [3151, 3003, 37]-code) | [i] | ||
| 36 | Linear OA(5143, 3151, F5, 34) (dual of [3151, 3008, 35]-code) | [i] | ||
| 37 | Linear OA(5138, 3151, F5, 33) (dual of [3151, 3013, 34]-code) | [i] | ||
| 38 | Linear OA(5133, 3151, F5, 32) (dual of [3151, 3018, 33]-code) | [i] | ||
| 39 | Linear OA(5128, 3151, F5, 31) (dual of [3151, 3023, 32]-code) | [i] | ||
| 40 | Linear OA(5123, 3151, F5, 29) (dual of [3151, 3028, 30]-code) | [i] | ||
| 41 | Linear OA(5118, 3151, F5, 28) (dual of [3151, 3033, 29]-code) | [i] | ||
| 42 | Linear OA(5113, 3151, F5, 27) (dual of [3151, 3038, 28]-code) | [i] | ||
| 43 | Linear OA(5108, 3151, F5, 26) (dual of [3151, 3043, 27]-code) | [i] | ||
| 44 | Linear OA(5103, 3151, F5, 24) (dual of [3151, 3048, 25]-code) | [i] | ||
| 45 | Linear OA(598, 3151, F5, 23) (dual of [3151, 3053, 24]-code) | [i] | ||
| 46 | Linear OA(593, 3151, F5, 22) (dual of [3151, 3058, 23]-code) | [i] | ||
| 47 | Linear OA(588, 3151, F5, 21) (dual of [3151, 3063, 22]-code) | [i] | ||
| 48 | Linear OA(583, 3151, F5, 19) (dual of [3151, 3068, 20]-code) | [i] | ||
| 49 | Linear OA(578, 3151, F5, 18) (dual of [3151, 3073, 19]-code) | [i] | ||
| 50 | Linear OA(573, 3151, F5, 17) (dual of [3151, 3078, 18]-code) | [i] | ||
| 51 | Linear OA(568, 3151, F5, 16) (dual of [3151, 3083, 17]-code) | [i] | ||
| 52 | Linear OA(563, 3151, F5, 14) (dual of [3151, 3088, 15]-code) | [i] | ||
| 53 | Linear OA(558, 3151, F5, 13) (dual of [3151, 3093, 14]-code) | [i] | ||
| 54 | Linear OA(553, 3151, F5, 12) (dual of [3151, 3098, 13]-code) | [i] | ||
| 55 | Linear OA(5138, 655, F5, 41) (dual of [655, 517, 42]-code) | [i] | Construction XX with a Chain of Extended Narrow-Sense BCH Codes | |
| 56 | Linear OA(5122, 655, F5, 36) (dual of [655, 533, 37]-code) | [i] | ||
| 57 | Linear OA(5111, 656, F5, 32) (dual of [656, 545, 33]-code) | [i] | ||
| 58 | Linear OA(592, 653, F5, 26) (dual of [653, 561, 27]-code) | [i] | ||
| 59 | Linear OA(592, 655, F5, 26) (dual of [655, 563, 27]-code) | [i] | ||
| 60 | Linear OA(576, 655, F5, 21) (dual of [655, 579, 22]-code) | [i] | ||