Information on Result #1297483
Linear OA(2215, 341, F2, 58) (dual of [341, 126, 59]-code), using construction X with Varšamov bound based on
- linear OA(2210, 334, F2, 58) (dual of [334, 124, 59]-code), using
- 1 times truncation [i] based on linear OA(2211, 335, F2, 59) (dual of [335, 124, 60]-code), using
- concatenation of two codes [i] based on
- linear OA(1636, 67, F16, 29) (dual of [67, 31, 30]-code), using
- construction X applied to AG(F,34P) ⊂ AG(F,36P) [i] based on
- linear OA(1635, 64, F16, 29) (dual of [64, 29, 30]-code), using algebraic-geometric code AG(F,34P) [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(1633, 64, F16, 27) (dual of [64, 31, 28]-code), using algebraic-geometric code AG(F,36P) [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
- linear OA(1635, 64, F16, 29) (dual of [64, 29, 30]-code), using algebraic-geometric code AG(F,34P) [i] based on function field F/F16 with g(F) = 6 and N(F) ≥ 65, using
- construction X applied to AG(F,34P) ⊂ AG(F,36P) [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(1636, 67, F16, 29) (dual of [67, 31, 30]-code), using
- concatenation of two codes [i] based on
- 1 times truncation [i] based on linear OA(2211, 335, F2, 59) (dual of [335, 124, 60]-code), using
- linear OA(2210, 336, F2, 55) (dual of [336, 126, 56]-code), using Gilbert–Varšamov bound and bm = 2210 > Vbs−1(k−1) = 1312 953779 268409 656159 885100 614771 377141 953607 618823 105759 798644 [i]
- linear OA(23, 5, F2, 2) (dual of [5, 2, 3]-code), using
- discarding factors / shortening the dual code based on linear OA(23, 7, F2, 2) (dual of [7, 4, 3]-code), using
- Hamming code H(3,2) [i]
- discarding factors / shortening the dual code based on linear OA(23, 7, F2, 2) (dual of [7, 4, 3]-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(2216, 342, F2, 59) (dual of [342, 126, 60]-code) | [i] | Adding a Parity Check Bit | |