Information on Result #661503
Linear OA(4172, 328, F4, 57) (dual of [328, 156, 58]-code), using concatenation of two codes based on
- linear OA(6430, 82, F64, 28) (dual of [82, 52, 29]-code), using
- construction X applied to AG(F,50P) ⊂ AG(F,52P) [i] based on
- linear OA(6429, 79, F64, 28) (dual of [79, 50, 29]-code), using algebraic-geometric code AG(F,50P) [i] based on function field F/F64 with g(F) = 1 and N(F) ≥ 80, using
- linear OA(6427, 79, F64, 26) (dual of [79, 52, 27]-code), using algebraic-geometric code AG(F,52P) [i] based on function field F/F64 with g(F) = 1 and N(F) ≥ 80 (see above)
- linear OA(641, 3, F64, 1) (dual of [3, 2, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(641, s, F64, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
- construction X applied to AG(F,50P) ⊂ AG(F,52P) [i] based on
- linear OA(41, 4, F4, 1) (dual of [4, 3, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(41, s, F4, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
Mode: Constructive and 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(4172, 328, F4, 56) (dual of [328, 156, 57]-code) | [i] | Strength Reduction | |
| 2 | Linear OA(4173, 329, F4, 57) (dual of [329, 156, 58]-code) | [i] | Code Embedding in Larger Space | |
| 3 | Linear OA(4174, 330, F4, 57) (dual of [330, 156, 58]-code) | [i] | ||
| 4 | Linear OA(4175, 331, F4, 57) (dual of [331, 156, 58]-code) | [i] | ||
| 5 | Linear OA(4171, 327, F4, 56) (dual of [327, 156, 57]-code) | [i] | Truncation | |
| 6 | Linear OOA(4172, 164, F4, 2, 57) (dual of [(164, 2), 156, 58]-NRT-code) | [i] | OOA Folding | |
| 7 | Linear OOA(4172, 109, F4, 3, 57) (dual of [(109, 3), 155, 58]-NRT-code) | [i] | ||