Information on Result #724391
Linear OA(2593, 676, F25, 40) (dual of [676, 583, 41]-code), using construction XX applied to C1 = C([620,26]), C2 = C([6,35]), C3 = C1 + C2 = C([6,26]), and C∩ = C1 ∩ C2 = C([620,35]) based on
- linear OA(2558, 624, F25, 31) (dual of [624, 566, 32]-code), using the primitive BCH-code C(I) with length 624 = 252−1, defining interval I = {−4,−3,…,26}, and designed minimum distance d ≥ |I|+1 = 32 [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 = {6,7,…,35}, 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 = {−4,−3,…,35}, and designed minimum distance d ≥ |I|+1 = 41 [i]
- linear OA(2541, 624, F25, 21) (dual of [624, 583, 22]-code), using the primitive BCH-code C(I) with length 624 = 252−1, defining interval I = {6,7,…,26}, and designed minimum distance d ≥ |I|+1 = 22 [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(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 (see above)
- 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)
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 OA(2594, 677, F25, 40) (dual of [677, 583, 41]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OOA(2593, 338, F25, 2, 40) (dual of [(338, 2), 583, 41]-NRT-code) | [i] | OOA Folding | |