Information on Result #661763
Linear OA(1678, 82, F16, 70) (dual of [82, 4, 71]-code), using juxtaposition based on
- linear OA(1611, 15, F16, 11) (dual of [15, 4, 12]-code or 15-arc in PG(10,16)), using
- discarding factors / shortening the dual code based on linear OA(1611, 16, F16, 11) (dual of [16, 5, 12]-code or 16-arc in PG(10,16)), using
- Reed–Solomon code RS(5,16) [i]
- discarding factors / shortening the dual code based on linear OA(1611, 16, F16, 11) (dual of [16, 5, 12]-code or 16-arc in PG(10,16)), using
- linear OA(1663, 67, F16, 58) (dual of [67, 4, 59]-code), using
- construction X applied to AG(F,5P) ⊂ AG(F,8P) [i] based on
- linear OA(1661, 64, F16, 58) (dual of [64, 3, 59]-code), using algebraic-geometric code AG(F,5P) 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(1660, 64, F16, 55) (dual of [64, 4, 56]-code), using algebraic-geometric code AG(F,8P) with known gap numbers [i] based on function field F/F16 with g(F) = 6 and N(F) ≥ 65 (see above)
- linear OA(162, 3, F16, 2) (dual of [3, 1, 3]-code or 3-arc in PG(1,16)), using
- dual of repetition code with length 3 [i]
- construction X applied to AG(F,5P) ⊂ AG(F,8P) [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(1678, 82, F16, 69) (dual of [82, 4, 70]-code) | [i] | Strength Reduction | |
| 2 | Linear OOA(1678, 41, F16, 2, 70) (dual of [(41, 2), 4, 71]-NRT-code) | [i] | OOA Folding | |