Information on Result #671872
Linear OA(25625, 65796, F256, 10) (dual of [65796, 65771, 11]-code), using (u, u+v)-construction based on
- linear OA(2566, 260, F256, 5) (dual of [260, 254, 6]-code), using
- construction X applied to AG(F, Q+124P) ⊂ AG(F, Q+125P) [i] based on
- 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, using the rational function field F256(x) [i]
- linear OA(2563, 257, F256, 3) (dual of [257, 254, 4]-code or 257-arc in PG(2,256) or 257-cap in PG(2,256)), using algebraic-geometric code AG(F, Q+125P) 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+124P) ⊂ AG(F, Q+125P) [i] based on
- linear OA(25619, 65536, F256, 10) (dual of [65536, 65517, 11]-code), using
- an extension Ce(9) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,9], and designed minimum distance d ≥ |I|+1 = 10 [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 OOA(25625, 21932, F256, 3, 10) (dual of [(21932, 3), 65771, 11]-NRT-code) | [i] | OOA Folding | |