Information on Result #724504
Linear OA(2597, 676, F25, 42) (dual of [676, 579, 43]-code), using construction XX applied to C1 = C([618,26]), C2 = C([4,35]), C3 = C1 + C2 = C([4,26]), and C∩ = C1 ∩ C2 = C([618,35]) based on
- linear OA(2562, 624, F25, 33) (dual of [624, 562, 34]-code), using the primitive BCH-code C(I) with length 624 = 252−1, defining interval I = {−6,−5,…,26}, and designed minimum distance d ≥ |I|+1 = 34 [i]
- linear OA(2563, 624, F25, 32) (dual of [624, 561, 33]-code), using the primitive BCH-code C(I) with length 624 = 252−1, defining interval I = {4,5,…,35}, and designed minimum distance d ≥ |I|+1 = 33 [i]
- linear OA(2580, 624, F25, 42) (dual of [624, 544, 43]-code), using the primitive BCH-code C(I) with length 624 = 252−1, defining interval I = {−6,−5,…,35}, and designed minimum distance d ≥ |I|+1 = 43 [i]
- linear OA(2545, 624, F25, 23) (dual of [624, 579, 24]-code), using the primitive BCH-code C(I) with length 624 = 252−1, defining interval I = {4,5,…,26}, and designed minimum distance d ≥ |I|+1 = 24 [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(2598, 677, F25, 42) (dual of [677, 579, 43]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OOA(2597, 338, F25, 2, 42) (dual of [(338, 2), 579, 43]-NRT-code) | [i] | OOA Folding | |