Information on Result #723603
Linear OA(2566, 657, F25, 29) (dual of [657, 591, 30]-code), using construction XX applied to C1 = C([623,25]), C2 = C([10,27]), C3 = C1 + C2 = C([10,25]), and C∩ = C1 ∩ C2 = C([623,27]) based on
- linear OA(2551, 624, F25, 27) (dual of [624, 573, 28]-code), using the primitive BCH-code C(I) with length 624 = 252−1, defining interval I = {−1,0,…,25}, and designed minimum distance d ≥ |I|+1 = 28 [i]
- linear OA(2535, 624, F25, 18) (dual of [624, 589, 19]-code), using the primitive BCH-code C(I) with length 624 = 252−1, defining interval I = {10,11,…,27}, and designed minimum distance d ≥ |I|+1 = 19 [i]
- 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 = {−1,0,…,27}, and designed minimum distance d ≥ |I|+1 = 30 [i]
- linear OA(2532, 624, F25, 16) (dual of [624, 592, 17]-code), using the primitive BCH-code C(I) with length 624 = 252−1, defining interval I = {10,11,…,25}, and designed minimum distance d ≥ |I|+1 = 17 [i]
- linear OA(2511, 29, F25, 10) (dual of [29, 18, 11]-code), using
- construction X applied to AG(F, Q+6P) ⊂ AG(F, Q+7P) [i] based on
- linear OA(2510, 26, F25, 10) (dual of [26, 16, 11]-code or 26-arc in PG(9,25)), using algebraic-geometric code AG(F, Q+6P) 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(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 (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, Q+6P) ⊂ AG(F, Q+7P) [i] based on
- linear OA(251, 4, F25, 1) (dual of [4, 3, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(251, 25, F25, 1) (dual of [25, 24, 2]-code), using
- Reed–Solomon code RS(24,25) [i]
- discarding factors / shortening the dual code based on linear OA(251, 25, F25, 1) (dual of [25, 24, 2]-code), 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.