Information on Result #723385
Linear OA(2556, 660, F25, 23) (dual of [660, 604, 24]-code), using construction XX applied to C1 = C([4,22]), C2 = C([0,13]), C3 = C1 + C2 = C([4,13]), and C∩ = C1 ∩ C2 = C([0,22]) based on
- linear OA(2538, 624, F25, 19) (dual of [624, 586, 20]-code), using the primitive BCH-code C(I) with length 624 = 252−1, defining interval I = {4,5,…,22}, and designed minimum distance d ≥ |I|+1 = 20 [i]
- linear OA(2527, 624, F25, 14) (dual of [624, 597, 15]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 624 = 252−1, defining interval I = [0,13], and designed minimum distance d ≥ |I|+1 = 15 [i]
- linear OA(2545, 624, F25, 23) (dual of [624, 579, 24]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 624 = 252−1, defining interval I = [0,22], and designed minimum distance d ≥ |I|+1 = 24 [i]
- linear OA(2520, 624, F25, 10) (dual of [624, 604, 11]-code), using the primitive BCH-code C(I) with length 624 = 252−1, defining interval I = {4,5,…,13}, and designed minimum distance d ≥ |I|+1 = 11 [i]
- linear OA(258, 26, F25, 8) (dual of [26, 18, 9]-code or 26-arc in PG(7,25)), using
- extended Reed–Solomon code RSe(18,25) [i]
- 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, using the rational function field F25(x) [i]
- algebraic-geometric code AG(F, Q+5P) with degQ = 2 and degPÂ =Â 3 [i] based on function field F/F25 with g(F) = 0 and N(F) ≥ 26 (see above)
- linear OA(253, 10, F25, 3) (dual of [10, 7, 4]-code or 10-arc in PG(2,25) or 10-cap in PG(2,25)), using
- discarding factors / shortening the dual code based on linear OA(253, 25, F25, 3) (dual of [25, 22, 4]-code or 25-arc in PG(2,25) or 25-cap in PG(2,25)), using
- Reed–Solomon code RS(22,25) [i]
- discarding factors / shortening the dual code based on linear OA(253, 25, F25, 3) (dual of [25, 22, 4]-code or 25-arc in PG(2,25) or 25-cap in PG(2,25)), 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(2556, 330, F25, 2, 23) (dual of [(330, 2), 604, 24]-NRT-code) | [i] | OOA Folding | |