Information on Result #661558
Linear OA(8172, 246, F8, 87) (dual of [246, 74, 88]-code), using concatenation of two codes based on
- linear OA(6445, 82, F64, 43) (dual of [82, 37, 44]-code), using
- construction X applied to AG(F,35P) ⊂ AG(F,37P) [i] based on
- linear OA(6444, 79, F64, 43) (dual of [79, 35, 44]-code), using algebraic-geometric code AG(F,35P) [i] based on function field F/F64 with g(F) = 1 and N(F) ≥ 80, using
- linear OA(6442, 79, F64, 41) (dual of [79, 37, 42]-code), using algebraic-geometric code AG(F,37P) [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,35P) ⊂ AG(F,37P) [i] based on
- linear OA(81, 3, F8, 1) (dual of [3, 2, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(81, s, F8, 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(8172, 246, F8, 86) (dual of [246, 74, 87]-code) | [i] | Strength Reduction | |
| 2 | Linear OA(8173, 247, F8, 87) (dual of [247, 74, 88]-code) | [i] | Code Embedding in Larger Space | |
| 3 | Linear OA(8171, 245, F8, 86) (dual of [245, 74, 87]-code) | [i] | Truncation | |
| 4 | Linear OOA(8172, 123, F8, 2, 87) (dual of [(123, 2), 74, 88]-NRT-code) | [i] | OOA Folding | |