Information on Result #1297553
Linear OA(2226, 347, F2, 62) (dual of [347, 121, 63]-code), using construction X with Varšamov bound based on
- linear OA(2224, 344, F2, 62) (dual of [344, 120, 63]-code), using
- 1 times truncation [i] based on linear OA(2225, 345, F2, 63) (dual of [345, 120, 64]-code), using
- concatenation of two codes [i] based on
- linear OA(1639, 69, F16, 31) (dual of [69, 30, 32]-code), using
- construction X applied to AG(F,32P) ⊂ AG(F,35P) [i] based on
- linear OA(1637, 64, F16, 31) (dual of [64, 27, 32]-code), using algebraic-geometric code AG(F,32P) [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(1634, 64, F16, 28) (dual of [64, 30, 29]-code), using algebraic-geometric code AG(F,35P) [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(1637, 64, F16, 31) (dual of [64, 27, 32]-code), using algebraic-geometric code AG(F,32P) [i] based on function field F/F16 with g(F) = 6 and N(F) ≥ 65, using
- construction X applied to AG(F,32P) ⊂ AG(F,35P) [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(1639, 69, F16, 31) (dual of [69, 30, 32]-code), using
- concatenation of two codes [i] based on
- 1 times truncation [i] based on linear OA(2225, 345, F2, 63) (dual of [345, 120, 64]-code), using
- linear OA(2224, 345, F2, 60) (dual of [345, 121, 61]-code), using Gilbert–Varšamov bound and bm = 2224 > Vbs−1(k−1) = 20 917401 889583 940566 183197 118372 218006 067191 601173 591803 086498 006584 [i]
- linear OA(21, 2, F2, 1) (dual of [2, 1, 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 (see above)
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(2227, 348, F2, 63) (dual of [348, 121, 64]-code) | [i] | Adding a Parity Check Bit | |