Information on Result #661523
Linear OA(4241, 424, F4, 83) (dual of [424, 183, 84]-code), using concatenation of two codes based on
- linear OA(6445, 106, F64, 41) (dual of [106, 61, 42]-code), using
- construction X applied to AG(F,61P) ⊂ AG(F,63P) [i] based on
- linear OA(6444, 103, F64, 41) (dual of [103, 59, 42]-code), using algebraic-geometric code AG(F,61P) [i] based on function field F/F64 with g(F) = 3 and N(F) ≥ 104, using
- linear OA(6442, 103, F64, 39) (dual of [103, 61, 40]-code), using algebraic-geometric code AG(F,63P) [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,61P) ⊂ AG(F,63P) [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(4241, 424, F4, 82) (dual of [424, 183, 83]-code) | [i] | Strength Reduction | |
| 2 | Linear OA(4242, 425, F4, 83) (dual of [425, 183, 84]-code) | [i] | Code Embedding in Larger Space | |
| 3 | Linear OA(4243, 426, F4, 83) (dual of [426, 183, 84]-code) | [i] | ||
| 4 | Linear OA(4244, 427, F4, 83) (dual of [427, 183, 84]-code) | [i] | ||
| 5 | Linear OA(4240, 423, F4, 82) (dual of [423, 183, 83]-code) | [i] | Truncation | |
| 6 | Linear OOA(4241, 212, F4, 2, 83) (dual of [(212, 2), 183, 84]-NRT-code) | [i] | OOA Folding | |
| 7 | Linear OOA(4241, 141, F4, 3, 83) (dual of [(141, 3), 182, 84]-NRT-code) | [i] | ||