Information on Result #661541
Linear OA(5144, 204, F5, 67) (dual of [204, 60, 68]-code), using concatenation of two codes based on
- linear OA(2538, 68, F25, 33) (dual of [68, 30, 34]-code), using
- construction X applied to AG(F,31P) ⊂ AG(F,33P) [i] based on
- linear OA(2537, 65, F25, 33) (dual of [65, 28, 34]-code), using algebraic-geometric code AG(F,31P) [i] based on function field F/F25 with g(F) = 4 and N(F) ≥ 66, using
- linear OA(2535, 65, F25, 31) (dual of [65, 30, 32]-code), using algebraic-geometric code AG(F,33P) [i] based on function field F/F25 with g(F) = 4 and N(F) ≥ 66 (see above)
- linear OA(251, 3, F25, 1) (dual of [3, 2, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(251, s, F25, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
- construction X applied to AG(F,31P) ⊂ AG(F,33P) [i] based on
- linear OA(51, 3, F5, 1) (dual of [3, 2, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(51, s, F5, 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(5144, 204, F5, 66) (dual of [204, 60, 67]-code) | [i] | Strength Reduction | |
| 2 | Linear OA(5145, 205, F5, 67) (dual of [205, 60, 68]-code) | [i] | Code Embedding in Larger Space | |
| 3 | Linear OA(5146, 206, F5, 67) (dual of [206, 60, 68]-code) | [i] | ||
| 4 | Linear OA(5147, 207, F5, 67) (dual of [207, 60, 68]-code) | [i] | ||
| 5 | Linear OA(5143, 203, F5, 66) (dual of [203, 60, 67]-code) | [i] | Truncation | |
| 6 | Linear OOA(5144, 102, F5, 2, 67) (dual of [(102, 2), 60, 68]-NRT-code) | [i] | OOA Folding | |
| 7 | Linear OOA(5144, 68, F5, 3, 67) (dual of [(68, 3), 60, 68]-NRT-code) | [i] | ||