Information on Result #723332
Linear OA(2554, 660, F25, 22) (dual of [660, 606, 23]-code), using construction XX applied to C1 = C([4,21]), C2 = C([0,12]), C3 = C1 + C2 = C([4,12]), and C∩ = C1 ∩ C2 = C([0,21]) based on
- linear OA(2536, 624, F25, 18) (dual of [624, 588, 19]-code), using the primitive BCH-code C(I) with length 624 = 252−1, defining interval I = {4,5,…,21}, and designed minimum distance d ≥ |I|+1 = 19 [i]
- linear OA(2525, 624, F25, 13) (dual of [624, 599, 14]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 624 = 252−1, defining interval I = [0,12], and designed minimum distance d ≥ |I|+1 = 14 [i]
- linear OA(2543, 624, F25, 22) (dual of [624, 581, 23]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 624 = 252−1, defining interval I = [0,21], and designed minimum distance d ≥ |I|+1 = 23 [i]
- linear OA(2518, 624, F25, 9) (dual of [624, 606, 10]-code), using the primitive BCH-code C(I) with length 624 = 252−1, defining interval I = {4,5,…,12}, and designed minimum distance d ≥ |I|+1 = 10 [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(2554, 330, F25, 2, 22) (dual of [(330, 2), 606, 23]-NRT-code) | [i] | OOA Folding | |