Information on Result #736029
Linear OA(25638, 65802, F256, 15) (dual of [65802, 65764, 16]-code), using (u, u+v)-construction based on
- linear OA(2568, 260, F256, 7) (dual of [260, 252, 8]-code), using
- construction X applied to AG(F, Q+123P) ⊂ AG(F, Q+124P) [i] based on
- linear OA(2567, 257, F256, 7) (dual of [257, 250, 8]-code or 257-arc in PG(6,256)), using algebraic-geometric code AG(F, Q+123P) 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]
- linear OA(2565, 257, F256, 5) (dual of [257, 252, 6]-code or 257-arc in PG(4,256)), using algebraic-geometric code AG(F, Q+124P) 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(2561, 3, F256, 1) (dual of [3, 2, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(2561, s, F256, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
- construction X applied to AG(F, Q+123P) ⊂ AG(F, Q+124P) [i] based on
- linear OA(25630, 65542, F256, 15) (dual of [65542, 65512, 16]-code), using
- construction X applied to C([0,7]) ⊂ C([0,6]) [i] based on
- linear OA(25629, 65537, F256, 15) (dual of [65537, 65508, 16]-code), using the expurgated narrow-sense BCH-code C(I) with length 65537 | 2564−1, defining interval I = [0,7], and minimum distance d ≥ |{−7,−6,…,7}|+1 = 16 (BCH-bound) [i]
- linear OA(25625, 65537, F256, 13) (dual of [65537, 65512, 14]-code), using the expurgated narrow-sense BCH-code C(I) with length 65537 | 2564−1, defining interval I = [0,6], and minimum distance d ≥ |{−6,−5,…,6}|+1 = 14 (BCH-bound) [i]
- linear OA(2561, 5, F256, 1) (dual of [5, 4, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(2561, s, F256, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s (see above)
- construction X applied to C([0,7]) ⊂ C([0,6]) [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 OOA(25638, 32901, F256, 2, 15) (dual of [(32901, 2), 65764, 16]-NRT-code) | [i] | OOA Folding | |
| 2 | Linear OOA(25638, 21934, F256, 3, 15) (dual of [(21934, 3), 65764, 16]-NRT-code) | [i] | ||
| 3 | Linear OOA(25638, 9400, F256, 15, 15) (dual of [(9400, 15), 140962, 16]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |