Information on Result #723772
Linear OA(2577, 664, F25, 33) (dual of [664, 587, 34]-code), using construction XX applied to C1 = C([622,26]), C2 = C([10,30]), C3 = C1 + C2 = C([10,26]), and C∩ = C1 ∩ C2 = C([622,30]) based on
- linear OA(2554, 624, F25, 29) (dual of [624, 570, 30]-code), using the primitive BCH-code C(I) with length 624 = 252−1, defining interval I = {−2,−1,…,26}, and designed minimum distance d ≥ |I|+1 = 30 [i]
- linear OA(2541, 624, F25, 21) (dual of [624, 583, 22]-code), using the primitive BCH-code C(I) with length 624 = 252−1, defining interval I = {10,11,…,30}, and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(2562, 624, F25, 33) (dual of [624, 562, 34]-code), using the primitive BCH-code C(I) with length 624 = 252−1, defining interval I = {−2,−1,…,30}, and designed minimum distance d ≥ |I|+1 = 34 [i]
- linear OA(2533, 624, F25, 17) (dual of [624, 591, 18]-code), using the primitive BCH-code C(I) with length 624 = 252−1, defining interval I = {10,11,…,26}, and designed minimum distance d ≥ |I|+1 = 18 [i]
- linear OA(2512, 29, F25, 11) (dual of [29, 17, 12]-code), using
- construction X applied to AG(F,7P) ⊂ AG(F,8P) [i] based on
- linear OA(2511, 26, F25, 11) (dual of [26, 15, 12]-code or 26-arc in PG(10,25)), using algebraic-geometric code AG(F,7P) with 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(259, 26, F25, 9) (dual of [26, 17, 10]-code or 26-arc in PG(8,25)), using algebraic-geometric code AG(F,8P) with degPÂ =Â 2 [i] based on function field F/F25 with g(F) = 0 and N(F) ≥ 26 (see above)
- linear OA(251, 3, F25, 1) (dual of [3, 2, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(251, s, F25, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
- construction X applied to AG(F,7P) ⊂ AG(F,8P) [i] based on
- linear OA(253, 11, F25, 3) (dual of [11, 8, 4]-code or 11-arc in PG(2,25) or 11-cap in PG(2,25)), using
- discarding factors / shortening the dual code based on linear OA(253, 25, F25, 3) (dual of [25, 22, 4]-code or 25-arc in PG(2,25) or 25-cap in PG(2,25)), using
- Reed–Solomon code RS(22,25) [i]
- discarding factors / shortening the dual code based on linear OA(253, 25, F25, 3) (dual of [25, 22, 4]-code or 25-arc in PG(2,25) or 25-cap in PG(2,25)), 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
None.