Information on Result #2295889
Linear OA(2248, 349, F2, 73) (dual of [349, 101, 74]-code), using adding a parity check bit based on linear OA(2247, 348, F2, 72) (dual of [348, 101, 73]-code), using
- construction X with Varšamov bound [i] based on
- linear OA(2244, 344, F2, 72) (dual of [344, 100, 73]-code), using
- 1 times truncation [i] based on linear OA(2245, 345, F2, 73) (dual of [345, 100, 74]-code), using
- concatenation of two codes [i] based on
- linear OA(1644, 69, F16, 36) (dual of [69, 25, 37]-code), using
- construction X applied to AG(F,27P) ⊂ AG(F,30P) [i] based on
- 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, using
- the Hermitian function field over F16 [i]
- linear OA(1639, 64, F16, 33) (dual of [64, 25, 34]-code), using algebraic-geometric code AG(F,30P) [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(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, using
- construction X applied to AG(F,27P) ⊂ AG(F,30P) [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(1644, 69, F16, 36) (dual of [69, 25, 37]-code), using
- concatenation of two codes [i] based on
- 1 times truncation [i] based on linear OA(2245, 345, F2, 73) (dual of [345, 100, 74]-code), using
- linear OA(2244, 345, F2, 69) (dual of [345, 101, 70]-code), using Gilbert–Varšamov bound and bm = 2244 > Vbs−1(k−1) = 13 428378 304538 491096 665008 713032 038204 114266 858007 591408 452952 925901 572943 [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]
- linear OA(2244, 344, F2, 72) (dual of [344, 100, 73]-code), using
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(2248, 349, F2, 72) (dual of [349, 101, 73]-code) | [i] | Strength Reduction | |
| 2 | Linear OA(2249, 350, F2, 73) (dual of [350, 101, 74]-code) | [i] | Code Embedding in Larger Space | |