Information on Result #693950
Linear OA(2597, 659, F25, 42) (dual of [659, 562, 43]-code), using construction XX applied to C([0,21]) ⊂ C([0,16]) ⊂ C([0,15]) based on
- linear OA(2585, 626, F25, 43) (dual of [626, 541, 44]-code), using the expurgated narrow-sense BCH-code C(I) with length 626 | 254−1, defining interval I = [0,21], and minimum distance d ≥ |{−21,−20,…,21}|+1 = 44 (BCH-bound) [i]
- linear OA(2565, 626, F25, 33) (dual of [626, 561, 34]-code), using the expurgated narrow-sense BCH-code C(I) with length 626 | 254−1, defining interval I = [0,16], and minimum distance d ≥ |{−16,−15,…,16}|+1 = 34 (BCH-bound) [i]
- linear OA(2561, 626, F25, 31) (dual of [626, 565, 32]-code), using the expurgated narrow-sense BCH-code C(I) with length 626 | 254−1, defining interval I = [0,15], and minimum distance d ≥ |{−15,−14,…,15}|+1 = 32 (BCH-bound) [i]
- linear OA(2510, 31, F25, 8) (dual of [31, 21, 9]-code), using
- construction X applied to AG(F, Q+5P) ⊂ AG(F, Q+6P) [i] based on
- linear OA(258, 26, F25, 8) (dual of [26, 18, 9]-code or 26-arc in PG(7,25)), using algebraic-geometric code AG(F, Q+7P) with degQ = 3 and degPÂ =Â 2 [i] based on function field F/F25 with g(F) = 0 and N(F) ≥ 26, using the rational function field F25(x) [i]
- linear OA(255, 26, F25, 5) (dual of [26, 21, 6]-code or 26-arc in PG(4,25)), using algebraic-geometric code AG(F,10P) with degPÂ =Â 2 [i] based on function field F/F25 with g(F) = 0 and N(F) ≥ 26 (see above)
- linear OA(252, 5, F25, 2) (dual of [5, 3, 3]-code or 5-arc in PG(1,25)), using
- discarding factors / shortening the dual code based on linear OA(252, 25, F25, 2) (dual of [25, 23, 3]-code or 25-arc in PG(1,25)), using
- Reed–Solomon code RS(23,25) [i]
- discarding factors / shortening the dual code based on linear OA(252, 25, F25, 2) (dual of [25, 23, 3]-code or 25-arc in PG(1,25)), using
- construction X applied to AG(F, Q+5P) ⊂ AG(F, Q+6P) [i] based on
- linear OA(251, 2, F25, 1) (dual of [2, 1, 2]-code), using
- dual of repetition code with length 2 [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
None.