Information on Result #732227
Linear OA(25104, 700, F25, 41) (dual of [700, 596, 42]-code), using (u, u+v)-construction based on
- linear OA(2524, 66, F25, 20) (dual of [66, 42, 21]-code), using
- extended algebraic-geometric code AGe(F,45P) [i] based on function field F/F25 with g(F) = 4 and N(F) ≥ 66, using
- linear OA(2580, 634, F25, 41) (dual of [634, 554, 42]-code), using
- construction XX applied to C1 = C([621,36]), C2 = C([0,37]), C3 = C1 + C2 = C([0,36]), and C∩ = C1 ∩ C2 = C([621,37]) [i] based on
- linear OA(2576, 624, F25, 40) (dual of [624, 548, 41]-code), using the primitive BCH-code C(I) with length 624 = 252−1, defining interval I = {−3,−2,…,36}, and designed minimum distance d ≥ |I|+1 = 41 [i]
- linear OA(2572, 624, F25, 38) (dual of [624, 552, 39]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 624 = 252−1, defining interval I = [0,37], and designed minimum distance d ≥ |I|+1 = 39 [i]
- 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 = {−3,−2,…,37}, and designed minimum distance d ≥ |I|+1 = 42 [i]
- linear OA(2570, 624, F25, 37) (dual of [624, 554, 38]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 624 = 252−1, defining interval I = [0,36], and designed minimum distance d ≥ |I|+1 = 38 [i]
- linear OA(252, 8, F25, 2) (dual of [8, 6, 3]-code or 8-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
- 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([621,36]), C2 = C([0,37]), C3 = C1 + C2 = C([0,36]), and C∩ = C1 ∩ C2 = C([621,37]) [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
The following results depend on this result:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | Linear OOA(25104, 350, F25, 2, 41) (dual of [(350, 2), 596, 42]-NRT-code) | [i] | OOA Folding | |