Information on Result #1297344
Linear OA(2175, 321, F2, 44) (dual of [321, 146, 45]-code), using construction X with Varšamov bound based on
- linear OA(2172, 317, F2, 44) (dual of [317, 145, 45]-code), using
- 1 times truncation [i] based on linear OA(2173, 318, F2, 45) (dual of [318, 145, 46]-code), using
- concatenation of two codes [i] based on
- linear OA(3224, 53, F32, 22) (dual of [53, 29, 23]-code), using
- extended algebraic-geometric code AGe(F,30P) [i] based on function field F/F32 with g(F) = 2 and N(F) ≥ 53, using
- linear OA(21, 6, F2, 1) (dual of [6, 5, 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(3224, 53, F32, 22) (dual of [53, 29, 23]-code), using
- concatenation of two codes [i] based on
- 1 times truncation [i] based on linear OA(2173, 318, F2, 45) (dual of [318, 145, 46]-code), using
- linear OA(2172, 318, F2, 41) (dual of [318, 146, 42]-code), using Gilbert–Varšamov bound and bm = 2172 > Vbs−1(k−1) = 1207 429158 160939 319050 278985 529844 682459 284538 923115 [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(2176, 322, F2, 45) (dual of [322, 146, 46]-code) | [i] | Adding a Parity Check Bit | |