Information on Result #724372
Linear OA(2592, 672, F25, 40) (dual of [672, 580, 41]-code), using construction XX applied to C1 = C([618,25]), C2 = C([4,33]), C3 = C1 + C2 = C([4,25]), and C∩ = C1 ∩ C2 = C([618,33]) based on
- linear OA(2561, 624, F25, 32) (dual of [624, 563, 33]-code), using the primitive BCH-code C(I) with length 624 = 252−1, defining interval I = {−6,−5,…,25}, and designed minimum distance d ≥ |I|+1 = 33 [i]
- linear OA(2559, 624, F25, 30) (dual of [624, 565, 31]-code), using the primitive BCH-code C(I) with length 624 = 252−1, defining interval I = {4,5,…,33}, and designed minimum distance d ≥ |I|+1 = 31 [i]
- linear OA(2576, 624, F25, 40) (dual of [624, 548, 41]-code), using the primitive BCH-code C(I) with length 624 = 252−1, defining interval I = {−6,−5,…,33}, and designed minimum distance d ≥ |I|+1 = 41 [i]
- linear OA(2544, 624, F25, 22) (dual of [624, 580, 23]-code), using the primitive BCH-code C(I) with length 624 = 252−1, defining interval I = {4,5,…,25}, and designed minimum distance d ≥ |I|+1 = 23 [i]
- linear OA(259, 26, F25, 9) (dual of [26, 17, 10]-code or 26-arc in PG(8,25)), using
- extended Reed–Solomon code RSe(17,25) [i]
- the expurgated narrow-sense BCH-code C(I) with length 26 | 252−1, defining interval I = [0,4], and minimum distance d ≥ |{−4,−3,…,4}|+1 = 10 (BCH-bound) [i]
- algebraic-geometric code AG(F,8P) with 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+4P) with degQ = 4 and degPÂ =Â 3 [i] based on function field F/F25 with g(F) = 0 and N(F) ≥ 26 (see above)
- linear OA(257, 22, F25, 7) (dual of [22, 15, 8]-code or 22-arc in PG(6,25)), using
- discarding factors / shortening the dual code based on linear OA(257, 25, F25, 7) (dual of [25, 18, 8]-code or 25-arc in PG(6,25)), using
- Reed–Solomon code RS(18,25) [i]
- discarding factors / shortening the dual code based on linear OA(257, 25, F25, 7) (dual of [25, 18, 8]-code or 25-arc in PG(6,25)), 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(2592, 336, F25, 2, 40) (dual of [(336, 2), 580, 41]-NRT-code) | [i] | OOA Folding | |