Information on Result #661227
Linear OA(1692, 524, F16, 44) (dual of [524, 432, 45]-code), using trace code based on linear OA(25646, 262, F256, 44) (dual of [262, 216, 45]-code), using
- construction X applied to AG(F, Q+70P) ⊂ AG(F, Q+71P) [i] based on
- linear OA(25644, 257, F256, 44) (dual of [257, 213, 45]-code or 257-arc in PG(43,256)), using algebraic-geometric code AG(F,106P) with 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]
- linear OA(25641, 257, F256, 41) (dual of [257, 216, 42]-code or 257-arc in PG(40,256)), using algebraic-geometric code AG(F, Q+106P) with degQ = 3 and degPÂ =Â 2 [i] based on function field F/F256 with g(F) = 0 and N(F) ≥ 257 (see above)
- linear OA(2562, 5, F256, 2) (dual of [5, 3, 3]-code or 5-arc in PG(1,256)), using
- discarding factors / shortening the dual code based on linear OA(2562, 256, F256, 2) (dual of [256, 254, 3]-code or 256-arc in PG(1,256)), using
- Reed–Solomon code RS(254,256) [i]
- discarding factors / shortening the dual code based on linear OA(2562, 256, F256, 2) (dual of [256, 254, 3]-code or 256-arc in PG(1,256)), 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(1693, 525, F16, 44) (dual of [525, 432, 45]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OOA(1692, 262, F16, 2, 44) (dual of [(262, 2), 432, 45]-NRT-code) | [i] | OOA Folding | |