Information on Result #724933
Linear OA(25110, 654, F25, 54) (dual of [654, 544, 55]-code), using construction XX applied to C1 = C([0,51]), C2 = C([11,53]), C3 = C1 + C2 = C([11,51]), and C∩ = C1 ∩ C2 = C([0,53]) based on
- linear OA(2596, 624, F25, 52) (dual of [624, 528, 53]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 624 = 252−1, defining interval I = [0,51], and designed minimum distance d ≥ |I|+1 = 53 [i]
- linear OA(2582, 624, F25, 43) (dual of [624, 542, 44]-code), using the primitive BCH-code C(I) with length 624 = 252−1, defining interval I = {11,12,…,53}, and designed minimum distance d ≥ |I|+1 = 44 [i]
- linear OA(2599, 624, F25, 54) (dual of [624, 525, 55]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 624 = 252−1, defining interval I = [0,53], and designed minimum distance d ≥ |I|+1 = 55 [i]
- linear OA(2579, 624, F25, 41) (dual of [624, 545, 42]-code), using the primitive BCH-code C(I) with length 624 = 252−1, defining interval I = {11,12,…,51}, and designed minimum distance d ≥ |I|+1 = 42 [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(251, 4, F25, 1) (dual of [4, 3, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(251, 25, F25, 1) (dual of [25, 24, 2]-code), using
- Reed–Solomon code RS(24,25) [i]
- discarding factors / shortening the dual code based on linear OA(251, 25, F25, 1) (dual of [25, 24, 2]-code), 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, 327, F25, 2, 54) (dual of [(327, 2), 544, 55]-NRT-code) | [i] | OOA Folding |