Information on Result #661737
Linear OA(16130, 138, F16, 108) (dual of [138, 8, 109]-code), using juxtaposition based on
- linear OA(1660, 68, F16, 53) (dual of [68, 8, 54]-code), using
- construction X applied to AG(F,10P) ⊂ AG(F,13P) [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(1656, 64, F16, 50) (dual of [64, 8, 51]-code), using algebraic-geometric code AG(F,13P) [i] based on function field F/F16 with g(F) = 6 and N(F) ≥ 65 (see above)
- linear OA(162, 4, F16, 2) (dual of [4, 2, 3]-code or 4-arc in PG(1,16)), using
- discarding factors / shortening the dual code based on linear OA(162, 16, F16, 2) (dual of [16, 14, 3]-code or 16-arc in PG(1,16)), using
- Reed–Solomon code RS(14,16) [i]
- discarding factors / shortening the dual code based on linear OA(162, 16, F16, 2) (dual of [16, 14, 3]-code or 16-arc in PG(1,16)), using
- construction X applied to AG(F,10P) ⊂ AG(F,13P) [i] based on
- linear OA(1662, 70, F16, 54) (dual of [70, 8, 55]-code), using
- construction X applied to AG(F,9P) ⊂ AG(F,13P) [i] based on
- linear OA(1659, 64, F16, 54) (dual of [64, 5, 55]-code), using algebraic-geometric code AG(F,9P) with known gap numbers [i] based on function field F/F16 with g(F) = 6 and N(F) ≥ 65 (see above)
- linear OA(1656, 64, F16, 50) (dual of [64, 8, 51]-code) (see above)
- linear OA(163, 6, F16, 3) (dual of [6, 3, 4]-code or 6-arc in PG(2,16) or 6-cap in PG(2,16)), using
- discarding factors / shortening the dual code based on linear OA(163, 16, F16, 3) (dual of [16, 13, 4]-code or 16-arc in PG(2,16) or 16-cap in PG(2,16)), using
- Reed–Solomon code RS(13,16) [i]
- discarding factors / shortening the dual code based on linear OA(163, 16, F16, 3) (dual of [16, 13, 4]-code or 16-arc in PG(2,16) or 16-cap in PG(2,16)), using
- construction X applied to AG(F,9P) ⊂ AG(F,13P) [i] based on
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(16130, 138, F16, 107) (dual of [138, 8, 108]-code) | [i] | Strength Reduction | |
| 2 | Linear OA(16129, 137, F16, 107) (dual of [137, 8, 108]-code) | [i] | Truncation | |
| 3 | Linear OA(16127, 135, F16, 105) (dual of [135, 8, 106]-code) | [i] | ||
| 4 | Linear OOA(16130, 69, F16, 2, 108) (dual of [(69, 2), 8, 109]-NRT-code) | [i] | OOA Folding | |