Information on Result #1297813
Linear OA(2259, 348, F2, 78) (dual of [348, 89, 79]-code), using construction X with Varšamov bound based on
- linear OA(2256, 344, F2, 78) (dual of [344, 88, 79]-code), using
- 1 times truncation [i] based on linear OA(2257, 345, F2, 79) (dual of [345, 88, 80]-code), using
- concatenation of two codes [i] based on
- linear OA(1647, 69, F16, 39) (dual of [69, 22, 40]-code), using
- construction X applied to AG(F,24P) ⊂ AG(F,27P) [i] based on
- linear OA(1645, 64, F16, 39) (dual of [64, 19, 40]-code), using algebraic-geometric code AG(F,24P) [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(1642, 64, F16, 36) (dual of [64, 22, 37]-code), using algebraic-geometric code AG(F,27P) [i] based on function field F/F16 with g(F) = 6 and N(F) ≥ 65 (see above)
- linear OA(162, 5, F16, 2) (dual of [5, 3, 3]-code or 5-arc in PG(1,16)), using
- discarding factors / shortening the dual code based on linear OA(162, 16, F16, 2) (dual of [16, 14, 3]-code or 16-arc in PG(1,16)), using
- Reed–Solomon code RS(14,16) [i]
- discarding factors / shortening the dual code based on linear OA(162, 16, F16, 2) (dual of [16, 14, 3]-code or 16-arc in PG(1,16)), using
- linear OA(1645, 64, F16, 39) (dual of [64, 19, 40]-code), using algebraic-geometric code AG(F,24P) [i] based on function field F/F16 with g(F) = 6 and N(F) ≥ 65, using
- construction X applied to AG(F,24P) ⊂ AG(F,27P) [i] based on
- linear OA(21, 5, F2, 1) (dual of [5, 4, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(21, s, F2, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
- linear OA(1647, 69, F16, 39) (dual of [69, 22, 40]-code), using
- concatenation of two codes [i] based on
- 1 times truncation [i] based on linear OA(2257, 345, F2, 79) (dual of [345, 88, 80]-code), using
- linear OA(2256, 345, F2, 75) (dual of [345, 89, 76]-code), using Gilbert–Varšamov bound and bm = 2256 > Vbs−1(k−1) = 43710 815908 170594 124831 202473 742150 651432 515469 868623 707635 026037 323985 263746 [i]
- linear OA(22, 3, F2, 2) (dual of [3, 1, 3]-code or 3-arc in PG(1,2)), using
- dual of repetition code with length 3 [i]
- Hamming code H(2,2) [i]
Mode: 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(2260, 349, F2, 79) (dual of [349, 89, 80]-code) | [i] | Adding a Parity Check Bit | |