Information on Result #724891
Linear OA(25110, 660, F25, 52) (dual of [660, 550, 53]-code), using construction XX applied to C1 = C([6,52]), C2 = C([1,41]), C3 = C1 + C2 = C([6,41]), and C∩ = C1 ∩ C2 = C([1,52]) based on
- linear OA(2590, 624, F25, 47) (dual of [624, 534, 48]-code), using the primitive BCH-code C(I) with length 624 = 252−1, defining interval I = {6,7,…,52}, and designed minimum distance d ≥ |I|+1 = 48 [i]
- linear OA(2579, 624, F25, 41) (dual of [624, 545, 42]-code), using the primitive narrow-sense BCH-code C(I) with length 624 = 252−1, defining interval I = [1,41], and designed minimum distance d ≥ |I|+1 = 42 [i]
- linear OA(2596, 624, F25, 52) (dual of [624, 528, 53]-code), using the primitive narrow-sense BCH-code C(I) with length 624 = 252−1, defining interval I = [1,52], and designed minimum distance d ≥ |I|+1 = 53 [i]
- linear OA(2571, 624, F25, 36) (dual of [624, 553, 37]-code), using the primitive BCH-code C(I) with length 624 = 252−1, defining interval I = {6,7,…,41}, and designed minimum distance d ≥ |I|+1 = 37 [i]
- linear OA(2510, 26, F25, 10) (dual of [26, 16, 11]-code or 26-arc in PG(9,25)), using
- extended Reed–Solomon code RSe(16,25) [i]
- 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]
- algebraic-geometric code AG(F,5P) with degPÂ =Â 3 [i] based on function field F/F25 with g(F) = 0 and N(F) ≥ 26 (see above)
- linear OA(254, 10, F25, 4) (dual of [10, 6, 5]-code or 10-arc in PG(3,25)), using
- discarding factors / shortening the dual code based on linear OA(254, 25, F25, 4) (dual of [25, 21, 5]-code or 25-arc in PG(3,25)), using
- Reed–Solomon code RS(21,25) [i]
- discarding factors / shortening the dual code based on linear OA(254, 25, F25, 4) (dual of [25, 21, 5]-code or 25-arc in PG(3,25)), 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(25110, 330, F25, 2, 52) (dual of [(330, 2), 550, 53]-NRT-code) | [i] | OOA Folding | |