Information on Result #724450
Linear OA(25101, 682, F25, 42) (dual of [682, 581, 43]-code), using construction XX applied to C1 = C([618,25]), C2 = C([5,35]), C3 = C1 + C2 = C([5,25]), and C∩ = C1 ∩ C2 = C([618,35]) based on
- linear OA(2561, 624, F25, 32) (dual of [624, 563, 33]-code), using the primitive BCH-code C(I) with length 624 = 252−1, defining interval I = {−6,−5,…,25}, and designed minimum distance d ≥ |I|+1 = 33 [i]
- linear OA(2561, 624, F25, 31) (dual of [624, 563, 32]-code), using the primitive BCH-code C(I) with length 624 = 252−1, defining interval I = {5,6,…,35}, and designed minimum distance d ≥ |I|+1 = 32 [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 = {−6,−5,…,35}, and designed minimum distance d ≥ |I|+1 = 43 [i]
- linear OA(2542, 624, F25, 21) (dual of [624, 582, 22]-code), using the primitive BCH-code C(I) with length 624 = 252−1, defining interval I = {5,6,…,25}, and designed minimum distance d ≥ |I|+1 = 22 [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(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 (see above)
- 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) (see above)
- construction X applied to AG(F,8P) ⊂ AG(F,9P) [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(25101, 341, F25, 2, 42) (dual of [(341, 2), 581, 43]-NRT-code) | [i] | OOA Folding | |