Information on Result #732188
Linear OA(25108, 696, F25, 43) (dual of [696, 588, 44]-code), using (u, u+v)-construction based on
- linear OA(2526, 68, F25, 21) (dual of [68, 42, 22]-code), using
- construction X applied to AG(F,43P) ⊂ AG(F,45P) [i] based on
- linear OA(2525, 65, F25, 21) (dual of [65, 40, 22]-code), using algebraic-geometric code AG(F,43P) [i] based on function field F/F25 with g(F) = 4 and N(F) ≥ 66, using
- linear OA(2523, 65, F25, 19) (dual of [65, 42, 20]-code), using algebraic-geometric code AG(F,45P) [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,43P) ⊂ AG(F,45P) [i] based on
- linear OA(2582, 628, F25, 43) (dual of [628, 546, 44]-code), using
- construction XX applied to C1 = C([623,40]), C2 = C([0,41]), C3 = C1 + C2 = C([0,40]), and C∩ = C1 ∩ C2 = C([623,41]) [i] based on
- 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 = {−1,0,…,40}, and designed minimum distance d ≥ |I|+1 = 43 [i]
- linear OA(2580, 624, F25, 42) (dual of [624, 544, 43]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 624 = 252−1, defining interval I = [0,41], and designed minimum distance d ≥ |I|+1 = 43 [i]
- linear OA(2582, 624, F25, 43) (dual of [624, 542, 44]-code), using the primitive BCH-code C(I) with length 624 = 252−1, defining interval I = {−1,0,…,41}, and designed minimum distance d ≥ |I|+1 = 44 [i]
- linear OA(2578, 624, F25, 41) (dual of [624, 546, 42]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 624 = 252−1, defining interval I = [0,40], and designed minimum distance d ≥ |I|+1 = 42 [i]
- 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
- linear OA(250, 2, F25, 0) (dual of [2, 2, 1]-code) (see above)
- construction XX applied to C1 = C([623,40]), C2 = C([0,41]), C3 = C1 + C2 = C([0,40]), and C∩ = C1 ∩ C2 = C([623,41]) [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(25108, 348, F25, 2, 43) (dual of [(348, 2), 588, 44]-NRT-code) | [i] | OOA Folding | |