Information on Result #732331
Linear OA(2593, 702, F25, 36) (dual of [702, 609, 37]-code), using (u, u+v)-construction based on
- linear OA(2523, 68, F25, 18) (dual of [68, 45, 19]-code), using
- construction X applied to AG(F,46P) ⊂ AG(F,48P) [i] based on
- linear OA(2522, 65, F25, 18) (dual of [65, 43, 19]-code), using algebraic-geometric code AG(F,46P) [i] based on function field F/F25 with g(F) = 4 and N(F) ≥ 66, using
- linear OA(2520, 65, F25, 16) (dual of [65, 45, 17]-code), using algebraic-geometric code AG(F,48P) [i] based on function field F/F25 with g(F) = 4 and N(F) ≥ 66 (see above)
- linear OA(251, 3, F25, 1) (dual of [3, 2, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(251, s, F25, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
- construction X applied to AG(F,46P) ⊂ AG(F,48P) [i] based on
- linear OA(2570, 634, F25, 36) (dual of [634, 564, 37]-code), using
- construction XX applied to C1 = C([621,31]), C2 = C([0,32]), C3 = C1 + C2 = C([0,31]), and C∩ = C1 ∩ C2 = C([621,32]) [i] based on
- linear OA(2566, 624, F25, 35) (dual of [624, 558, 36]-code), using the primitive BCH-code C(I) with length 624 = 252−1, defining interval I = {−3,−2,…,31}, and designed minimum distance d ≥ |I|+1 = 36 [i]
- linear OA(2562, 624, F25, 33) (dual of [624, 562, 34]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 624 = 252−1, defining interval I = [0,32], and designed minimum distance d ≥ |I|+1 = 34 [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 = {−3,−2,…,32}, and designed minimum distance d ≥ |I|+1 = 37 [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(252, 8, F25, 2) (dual of [8, 6, 3]-code or 8-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
- linear OA(250, 2, F25, 0) (dual of [2, 2, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(250, s, F25, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
- construction XX applied to C1 = C([621,31]), C2 = C([0,32]), C3 = C1 + C2 = C([0,31]), and C∩ = C1 ∩ C2 = C([621,32]) [i] based on
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(2593, 351, F25, 2, 36) (dual of [(351, 2), 609, 37]-NRT-code) | [i] | OOA Folding | |