Information on Result #732205
Linear OA(25109, 703, F25, 42) (dual of [703, 594, 43]-code), using (u, u+v)-construction based on
- linear OA(2528, 72, F25, 21) (dual of [72, 44, 22]-code), using
- construction X applied to AG(F,43P) ⊂ AG(F,47P) [i] based on
- linear OA(2525, 65, F25, 21) (dual of [65, 40, 22]-code), using algebraic-geometric code AG(F,43P) [i] based on function field F/F25 with g(F) = 4 and N(F) ≥ 66, using
- linear OA(2521, 65, F25, 17) (dual of [65, 44, 18]-code), using algebraic-geometric code AG(F,47P) [i] based on function field F/F25 with g(F) = 4 and N(F) ≥ 66 (see above)
- linear OA(253, 7, F25, 3) (dual of [7, 4, 4]-code or 7-arc in PG(2,25) or 7-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
- construction X applied to AG(F,43P) ⊂ AG(F,47P) [i] based on
- linear OA(2581, 631, F25, 42) (dual of [631, 550, 43]-code), using
- construction XX applied to C1 = C([622,38]), C2 = C([0,39]), C3 = C1 + C2 = C([0,38]), and C∩ = C1 ∩ C2 = C([622,39]) [i] based on
- linear OA(2578, 624, F25, 41) (dual of [624, 546, 42]-code), using the primitive BCH-code C(I) with length 624 = 252−1, defining interval I = {−2,−1,…,38}, and designed minimum distance d ≥ |I|+1 = 42 [i]
- linear OA(2576, 624, F25, 40) (dual of [624, 548, 41]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 624 = 252−1, defining interval I = [0,39], and designed minimum distance d ≥ |I|+1 = 41 [i]
- linear OA(2580, 624, F25, 42) (dual of [624, 544, 43]-code), using the primitive BCH-code C(I) with length 624 = 252−1, defining interval I = {−2,−1,…,39}, and designed minimum distance d ≥ |I|+1 = 43 [i]
- linear OA(2574, 624, F25, 39) (dual of [624, 550, 40]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 624 = 252−1, defining interval I = [0,38], and designed minimum distance d ≥ |I|+1 = 40 [i]
- linear OA(251, 5, F25, 1) (dual of [5, 4, 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
- linear OA(250, 2, F25, 0) (dual of [2, 2, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(250, s, F25, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
- construction XX applied to C1 = C([622,38]), C2 = C([0,39]), C3 = C1 + C2 = C([0,38]), and C∩ = C1 ∩ C2 = C([622,39]) [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
None.