Information on Result #661521
Linear OA(4238, 424, F4, 81) (dual of [424, 186, 82]-code), using concatenation of two codes based on
- linear OA(6444, 106, F64, 40) (dual of [106, 62, 41]-code), using
- construction X applied to AG(F,62P) ⊂ AG(F,64P) [i] based on
- linear OA(6443, 103, F64, 40) (dual of [103, 60, 41]-code), using algebraic-geometric code AG(F,62P) [i] based on function field F/F64 with g(F) = 3 and N(F) ≥ 104, using
- linear OA(6441, 103, F64, 38) (dual of [103, 62, 39]-code), using algebraic-geometric code AG(F,64P) [i] based on function field F/F64 with g(F) = 3 and N(F) ≥ 104 (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,62P) ⊂ AG(F,64P) [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(4238, 424, F4, 80) (dual of [424, 186, 81]-code) | [i] | Strength Reduction | |
| 2 | Linear OA(4239, 425, F4, 81) (dual of [425, 186, 82]-code) | [i] | Code Embedding in Larger Space | |
| 3 | Linear OA(4240, 426, F4, 81) (dual of [426, 186, 82]-code) | [i] | ||
| 4 | Linear OA(4241, 427, F4, 81) (dual of [427, 186, 82]-code) | [i] | ||
| 5 | Linear OA(4237, 423, F4, 80) (dual of [423, 186, 81]-code) | [i] | Truncation | |
| 6 | Linear OOA(4238, 212, F4, 2, 81) (dual of [(212, 2), 186, 82]-NRT-code) | [i] | OOA Folding | |
| 7 | Linear OOA(4238, 141, F4, 3, 81) (dual of [(141, 3), 185, 82]-NRT-code) | [i] | ||