Information on Result #723749
Linear OA(2567, 652, F25, 31) (dual of [652, 585, 32]-code), using construction XX applied to C1 = C([621,26]), C2 = C([7,27]), C3 = C1 + C2 = C([7,26]), and C∩ = C1 ∩ C2 = C([621,27]) based on
- linear OA(2556, 624, F25, 30) (dual of [624, 568, 31]-code), using the primitive BCH-code C(I) with length 624 = 252−1, defining interval I = {−3,−2,…,26}, and designed minimum distance d ≥ |I|+1 = 31 [i]
- linear OA(2541, 624, F25, 21) (dual of [624, 583, 22]-code), using the primitive BCH-code C(I) with length 624 = 252−1, defining interval I = {7,8,…,27}, and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(2558, 624, F25, 31) (dual of [624, 566, 32]-code), using the primitive BCH-code C(I) with length 624 = 252−1, defining interval I = {−3,−2,…,27}, and designed minimum distance d ≥ |I|+1 = 32 [i]
- linear OA(2539, 624, F25, 20) (dual of [624, 585, 21]-code), using the primitive BCH-code C(I) with length 624 = 252−1, defining interval I = {7,8,…,26}, 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(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
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(2567, 326, F25, 2, 31) (dual of [(326, 2), 585, 32]-NRT-code) | [i] | OOA Folding | |