Information on Result #724593
Linear OA(25102, 678, F25, 44) (dual of [678, 576, 45]-code), using construction XX applied to C1 = C([615,25]), C2 = C([1,34]), C3 = C1 + C2 = C([1,25]), and C∩ = C1 ∩ C2 = C([615,34]) based on
- linear OA(2567, 624, F25, 35) (dual of [624, 557, 36]-code), using the primitive BCH-code C(I) with length 624 = 252−1, defining interval I = {−9,−8,…,25}, and designed minimum distance d ≥ |I|+1 = 36 [i]
- linear OA(2565, 624, F25, 34) (dual of [624, 559, 35]-code), using the primitive narrow-sense BCH-code C(I) with length 624 = 252−1, defining interval I = [1,34], and designed minimum distance d ≥ |I|+1 = 35 [i]
- linear OA(2584, 624, F25, 44) (dual of [624, 540, 45]-code), using the primitive BCH-code C(I) with length 624 = 252−1, defining interval I = {−9,−8,…,34}, and designed minimum distance d ≥ |I|+1 = 45 [i]
- linear OA(2548, 624, F25, 25) (dual of [624, 576, 26]-code), using the primitive narrow-sense BCH-code C(I) with length 624 = 252−1, defining interval I = [1,25], and designed minimum distance d ≥ |I|+1 = 26 [i]
- linear OA(2510, 29, F25, 9) (dual of [29, 19, 10]-code), using
- construction X applied to AG(F,8P) ⊂ AG(F,9P) [i] based on
- 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, using the rational function field F25(x) [i]
- linear OA(257, 26, F25, 7) (dual of [26, 19, 8]-code or 26-arc in PG(6,25)), using algebraic-geometric code AG(F,9P) 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,8P) ⊂ AG(F,9P) [i] based on
- linear OA(258, 25, F25, 8) (dual of [25, 17, 9]-code or 25-arc in PG(7,25)), using
- Reed–Solomon code RS(17,25) [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
The following results depend on this result:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | Linear OOA(25102, 339, F25, 2, 44) (dual of [(339, 2), 576, 45]-NRT-code) | [i] | OOA Folding | |