Information on Result #644791
Linear OA(1622, 67, F16, 15) (dual of [67, 45, 16]-code), using construction X applied to AG(F,48P) ⊂ AG(F,50P) based on
- linear OA(1621, 64, F16, 15) (dual of [64, 43, 16]-code), using algebraic-geometric code AG(F,48P) [i] based on function field F/F16 with g(F) = 6 and N(F) ≥ 65, using
- the Hermitian function field over F16 [i]
- linear OA(1619, 64, F16, 13) (dual of [64, 45, 14]-code), using algebraic-geometric code AG(F,50P) [i] based on function field F/F16 with g(F) = 6 and N(F) ≥ 65 (see above)
- linear OA(161, 3, F16, 1) (dual of [3, 2, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(161, s, F16, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
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.
Other Results with Identical Parameters
None.
Depending Results
The following results depend on this result:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | Linear OA(444, 134, F4, 15) (dual of [134, 90, 16]-code) | [i] | Trace Code | |
| 2 | Linear OA(1684, 581, F16, 31) (dual of [581, 497, 32]-code) | [i] | (u, u+v)-Construction | |
| 3 | Linear OA(1686, 587, F16, 31) (dual of [587, 501, 32]-code) | [i] | ||
| 4 | Linear OA(16110, 4163, F16, 31) (dual of [4163, 4053, 32]-code) | [i] | ||
| 5 | Linear OA(1682, 581, F16, 30) (dual of [581, 499, 31]-code) | [i] | ||
| 6 | Linear OA(16107, 4163, F16, 30) (dual of [4163, 4056, 31]-code) | [i] | ||
| 7 | Linear OA(16110, 4166, F16, 31) (dual of [4166, 4056, 32]-code) | [i] | ||
| 8 | Linear OA(16111, 4170, F16, 31) (dual of [4170, 4059, 32]-code) | [i] | ||
| 9 | Linear OA(16112, 4174, F16, 31) (dual of [4174, 4062, 32]-code) | [i] | ||
| 10 | Linear OA(16113, 4178, F16, 31) (dual of [4178, 4065, 32]-code) | [i] | ||
| 11 | Linear OA(16107, 4166, F16, 30) (dual of [4166, 4059, 31]-code) | [i] | ||
| 12 | Linear OA(16108, 4170, F16, 30) (dual of [4170, 4062, 31]-code) | [i] | ||
| 13 | Linear OA(16109, 4174, F16, 30) (dual of [4174, 4065, 31]-code) | [i] | ||
| 14 | Linear OA(16128, 4163, F16, 38) (dual of [4163, 4035, 39]-code) | [i] | Construction X with Extended Narrow-Sense BCH Codes | |
| 15 | Linear OA(16125, 4163, F16, 37) (dual of [4163, 4038, 38]-code) | [i] | ||
| 16 | Linear OA(16122, 4163, F16, 36) (dual of [4163, 4041, 37]-code) | [i] | ||
| 17 | Linear OA(16119, 4163, F16, 35) (dual of [4163, 4044, 36]-code) | [i] | ||
| 18 | Linear OA(16116, 4163, F16, 34) (dual of [4163, 4047, 35]-code) | [i] | ||
| 19 | Linear OA(16113, 4163, F16, 33) (dual of [4163, 4050, 34]-code) | [i] | ||
| 20 | Linear OOA(1622, 33, F16, 2, 15) (dual of [(33, 2), 44, 16]-NRT-code) | [i] | OOA Folding | |