Information on Result #659040
Linear OA(16125, 132, F16, 107) (dual of [132, 7, 108]-code), using repeating each code word 2 times based on linear OA(1659, 66, F16, 53) (dual of [66, 7, 54]-code), using
- construction X applied to AG(F,10P) ⊂ AG(F,12P) [i] based on
- linear OA(1658, 64, F16, 53) (dual of [64, 6, 54]-code), using algebraic-geometric code AG(F,10P) with known gap numbers [i] based on function field F/F16 with g(F) = 6 and N(F) ≥ 65, using the Hermitian function field over F16 [i]
- linear OA(1657, 64, F16, 51) (dual of [64, 7, 52]-code), using algebraic-geometric code AG(F,12P) [i] based on function field F/F16 with g(F) = 6 and N(F) ≥ 65 (see above)
- linear OA(161, 2, F16, 1) (dual of [2, 1, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(161, s, F16, 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(16125, 132, F16, 106) (dual of [132, 7, 107]-code) | [i] | Strength Reduction | |
| 2 | Linear OA(16124, 131, F16, 106) (dual of [131, 7, 107]-code) | [i] | Truncation | |
| 3 | Linear OA(16122, 129, F16, 104) (dual of [129, 7, 105]-code) | [i] | ||
| 4 | Linear OA(16120, 127, F16, 102) (dual of [127, 7, 103]-code) | [i] | ||
| 5 | Linear OA(16118, 125, F16, 100) (dual of [125, 7, 101]-code) | [i] | ||
| 6 | Linear OA(16116, 123, F16, 98) (dual of [123, 7, 99]-code) | [i] | ||
| 7 | Linear OA(16114, 121, F16, 96) (dual of [121, 7, 97]-code) | [i] | ||
| 8 | Linear OA(16112, 119, F16, 94) (dual of [119, 7, 95]-code) | [i] | ||
| 9 | Linear OA(16110, 117, F16, 92) (dual of [117, 7, 93]-code) | [i] | ||
| 10 | Linear OOA(16125, 66, F16, 2, 107) (dual of [(66, 2), 7, 108]-NRT-code) | [i] | OOA Folding | |