Information on Result #724088
Linear OA(2582, 666, F25, 36) (dual of [666, 584, 37]-code), using construction XX applied to C1 = C([620,25]), C2 = C([6,31]), C3 = C1 + C2 = C([6,25]), and C∩ = C1 ∩ C2 = C([620,31]) based on
- linear OA(2557, 624, F25, 30) (dual of [624, 567, 31]-code), using the primitive BCH-code C(I) with length 624 = 252−1, defining interval I = {−4,−3,…,25}, and designed minimum distance d ≥ |I|+1 = 31 [i]
- linear OA(2551, 624, F25, 26) (dual of [624, 573, 27]-code), using the primitive BCH-code C(I) with length 624 = 252−1, defining interval I = {6,7,…,31}, and designed minimum distance d ≥ |I|+1 = 27 [i]
- linear OA(2568, 624, F25, 36) (dual of [624, 556, 37]-code), using the primitive BCH-code C(I) with length 624 = 252−1, defining interval I = {−4,−3,…,31}, and designed minimum distance d ≥ |I|+1 = 37 [i]
- linear OA(2540, 624, F25, 20) (dual of [624, 584, 21]-code), using the primitive BCH-code C(I) with length 624 = 252−1, defining interval I = {6,7,…,25}, and designed minimum distance d ≥ |I|+1 = 21 [i]
- linear OA(259, 26, F25, 9) (dual of [26, 17, 10]-code or 26-arc in PG(8,25)), using
- extended Reed–Solomon code RSe(17,25) [i]
- the expurgated narrow-sense BCH-code C(I) with length 26 | 252−1, defining interval I = [0,4], and minimum distance d ≥ |{−4,−3,…,4}|+1 = 10 (BCH-bound) [i]
- 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]
- algebraic-geometric code AG(F, Q+4P) with degQ = 4 and degPÂ =Â 3 [i] based on function field F/F25 with g(F) = 0 and N(F) ≥ 26 (see above)
- linear OA(255, 16, F25, 5) (dual of [16, 11, 6]-code or 16-arc in PG(4,25)), using
- discarding factors / shortening the dual code based on linear OA(255, 25, F25, 5) (dual of [25, 20, 6]-code or 25-arc in PG(4,25)), using
- Reed–Solomon code RS(20,25) [i]
- discarding factors / shortening the dual code based on linear OA(255, 25, F25, 5) (dual of [25, 20, 6]-code or 25-arc in PG(4,25)), 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
The following results depend on this result:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | Linear OOA(2582, 333, F25, 2, 36) (dual of [(333, 2), 584, 37]-NRT-code) | [i] | OOA Folding | |