Information on Result #724713
Linear OA(25100, 664, F25, 46) (dual of [664, 564, 47]-code), using construction XX applied to C1 = C([615,31]), C2 = C([0,36]), C3 = C1 + C2 = C([0,31]), and C∩ = C1 ∩ C2 = C([615,36]) based on
- linear OA(2578, 624, F25, 41) (dual of [624, 546, 42]-code), using the primitive BCH-code C(I) with length 624 = 252−1, defining interval I = {−9,−8,…,31}, and designed minimum distance d ≥ |I|+1 = 42 [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(2560, 624, F25, 32) (dual of [624, 564, 33]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 624 = 252−1, defining interval I = [0,31], and designed minimum distance d ≥ |I|+1 = 33 [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(254, 14, F25, 4) (dual of [14, 10, 5]-code or 14-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(25100, 332, F25, 2, 46) (dual of [(332, 2), 564, 47]-NRT-code) | [i] | OOA Folding | |