Information on Result #658597
Linear OA(1663, 67, F16, 58) (dual of [67, 4, 59]-code), using construction X applied to AG(F,5P) ⊂ AG(F,8P) 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]
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(1662, 66, F16, 57) (dual of [66, 4, 58]-code) | [i] | Truncation | |
| 2 | Linear OA(1661, 65, F16, 56) (dual of [65, 4, 57]-code) | [i] | ||
| 3 | Linear OA(16130, 134, F16, 117) (dual of [134, 4, 118]-code) | [i] | Repeating Each Code Word | |
| 4 | Linear OA(1678, 82, F16, 70) (dual of [82, 4, 71]-code) | [i] | Juxtaposition | |
| 5 | Linear OA(1679, 83, F16, 71) (dual of [83, 4, 72]-code) | [i] | ||
| 6 | Linear OA(1680, 84, F16, 72) (dual of [84, 4, 73]-code) | [i] | ||
| 7 | Linear OA(1685, 89, F16, 76) (dual of [89, 4, 77]-code) | [i] | ||
| 8 | Linear OA(1686, 90, F16, 77) (dual of [90, 4, 78]-code) | [i] | ||
| 9 | Linear OA(1687, 91, F16, 78) (dual of [91, 4, 79]-code) | [i] | ||
| 10 | Linear OA(1694, 98, F16, 84) (dual of [98, 4, 85]-code) | [i] | ||
| 11 | Linear OA(1695, 99, F16, 85) (dual of [99, 4, 86]-code) | [i] | ||
| 12 | Linear OA(1696, 100, F16, 86) (dual of [100, 4, 87]-code) | [i] | ||
| 13 | Linear OA(1699, 103, F16, 88) (dual of [103, 4, 89]-code) | [i] | ||
| 14 | Linear OA(16100, 104, F16, 89) (dual of [104, 4, 90]-code) | [i] | ||
| 15 | Linear OA(16101, 105, F16, 90) (dual of [105, 4, 91]-code) | [i] | ||
| 16 | Linear OA(16106, 110, F16, 94) (dual of [110, 4, 95]-code) | [i] | ||
| 17 | Linear OA(16107, 111, F16, 95) (dual of [111, 4, 96]-code) | [i] | ||
| 18 | Linear OA(16108, 112, F16, 96) (dual of [112, 4, 97]-code) | [i] | ||
| 19 | Linear OA(1688, 92, F16, 79) (dual of [92, 4, 80]-code) | [i] | ||