Information on Result #724052
Linear OA(2588, 680, F25, 36) (dual of [680, 592, 37]-code), using construction XX applied to C1 = C([623,25]), C2 = C([10,34]), C3 = C1 + C2 = C([10,25]), and C∩ = C1 ∩ C2 = C([623,34]) based on
- linear OA(2551, 624, F25, 27) (dual of [624, 573, 28]-code), using the primitive BCH-code C(I) with length 624 = 252−1, defining interval I = {−1,0,…,25}, and designed minimum distance d ≥ |I|+1 = 28 [i]
- linear OA(2549, 624, F25, 25) (dual of [624, 575, 26]-code), using the primitive BCH-code C(I) with length 624 = 252−1, defining interval I = {10,11,…,34}, and designed minimum distance d ≥ |I|+1 = 26 [i]
- linear OA(2568, 624, F25, 36) (dual of [624, 556, 37]-code), using the primitive BCH-code C(I) with length 624 = 252−1, defining interval I = {−1,0,…,34}, and designed minimum distance d ≥ |I|+1 = 37 [i]
- linear OA(2532, 624, F25, 16) (dual of [624, 592, 17]-code), using the primitive BCH-code C(I) with length 624 = 252−1, defining interval I = {10,11,…,25}, and designed minimum distance d ≥ |I|+1 = 17 [i]
- linear OA(2512, 31, F25, 10) (dual of [31, 19, 11]-code), using
- construction X applied to AG(F,5P) ⊂ AG(F,6P) [i] based on
- linear OA(2510, 26, F25, 10) (dual of [26, 16, 11]-code or 26-arc in PG(9,25)), using algebraic-geometric code AG(F, Q+6P) 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]
- linear OA(257, 26, F25, 7) (dual of [26, 19, 8]-code or 26-arc in PG(6,25)), using algebraic-geometric code AG(F,9P) with degPÂ =Â 2 [i] based on function field F/F25 with g(F) = 0 and N(F) ≥ 26 (see above)
- linear OA(252, 5, F25, 2) (dual of [5, 3, 3]-code or 5-arc in PG(1,25)), using
- discarding factors / shortening the dual code based on linear OA(252, 25, F25, 2) (dual of [25, 23, 3]-code or 25-arc in PG(1,25)), using
- Reed–Solomon code RS(23,25) [i]
- discarding factors / shortening the dual code based on linear OA(252, 25, F25, 2) (dual of [25, 23, 3]-code or 25-arc in PG(1,25)), using
- construction X applied to AG(F,5P) ⊂ AG(F,6P) [i] based on
- linear OA(258, 25, F25, 8) (dual of [25, 17, 9]-code or 25-arc in PG(7,25)), using
- Reed–Solomon code RS(17,25) [i]
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(2588, 340, F25, 2, 36) (dual of [(340, 2), 592, 37]-NRT-code) | [i] | OOA Folding | |