Information on Result #724725
Linear OA(2597, 655, F25, 46) (dual of [655, 558, 47]-code), using construction XX applied to C1 = C([615,34]), C2 = C([0,36]), C3 = C1 + C2 = C([0,34]), and C∩ = C1 ∩ C2 = C([615,36]) based on
- linear OA(2584, 624, F25, 44) (dual of [624, 540, 45]-code), using the primitive BCH-code C(I) with length 624 = 252−1, defining interval I = {−9,−8,…,34}, and designed minimum distance d ≥ |I|+1 = 45 [i]
- linear OA(2570, 624, F25, 37) (dual of [624, 554, 38]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 624 = 252−1, defining interval I = [0,36], and designed minimum distance d ≥ |I|+1 = 38 [i]
- linear OA(2588, 624, F25, 46) (dual of [624, 536, 47]-code), using the primitive BCH-code C(I) with length 624 = 252−1, defining interval I = {−9,−8,…,36}, and designed minimum distance d ≥ |I|+1 = 47 [i]
- linear OA(2566, 624, F25, 35) (dual of [624, 558, 36]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 624 = 252−1, defining interval I = [0,34], and designed minimum distance d ≥ |I|+1 = 36 [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(251, 5, F25, 1) (dual of [5, 4, 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(2597, 327, F25, 2, 46) (dual of [(327, 2), 557, 47]-NRT-code) | [i] | OOA Folding | |