Information on Result #629202
Linear OA(1658, 514, F16, 29) (dual of [514, 456, 30]-code), using trace code based on linear OA(25629, 257, F256, 29) (dual of [257, 228, 30]-code or 257-arc in PG(28,256)), using
- extended Reed–Solomon code RSe(228,256) [i]
- the expurgated narrow-sense BCH-code C(I) with length 257 | 2562−1, defining interval I = [0,14], and minimum distance d ≥ |{−14,−13,…,14}|+1 = 30 (BCH-bound) [i]
- algebraic-geometric code AG(F, Q+112P) with degQ = 3 and degPÂ =Â 2 [i] based on function field F/F256 with g(F) = 0 and N(F) ≥ 257, using the rational function field F256(x) [i]
- algebraic-geometric code AG(F, Q+75P) with degQ = 2 and degPÂ =Â 3 [i] based on function field F/F256 with g(F) = 0 and N(F) ≥ 257 (see above)
- algebraic-geometric code AG(F, Q+45P) with degQ = 2 and degPÂ =Â 5 [i] based on function field F/F256 with g(F) = 0 and N(F) ≥ 257 (see above)
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(1659, 515, F16, 29) (dual of [515, 456, 30]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OA(1675, 552, F16, 29) (dual of [552, 477, 30]-code) | [i] | (u, u+v)-Construction | |
| 3 | Linear OA(1676, 559, F16, 29) (dual of [559, 483, 30]-code) | [i] | ||
| 4 | Linear OA(1677, 563, F16, 29) (dual of [563, 486, 30]-code) | [i] | ||
| 5 | Linear OA(1678, 579, F16, 29) (dual of [579, 501, 30]-code) | [i] | ||
| 6 | Linear OA(1679, 581, F16, 29) (dual of [581, 502, 30]-code) | [i] | ||
| 7 | Linear OA(1680, 583, F16, 29) (dual of [583, 503, 30]-code) | [i] | ||
| 8 | Linear OOA(1658, 257, F16, 2, 29) (dual of [(257, 2), 456, 30]-NRT-code) | [i] | OOA Folding | |