Information on Result #732687
Linear OA(2559, 696, F25, 22) (dual of [696, 637, 23]-code), using (u, u+v)-construction based on
- linear OA(2516, 68, F25, 11) (dual of [68, 52, 12]-code), using
- construction X applied to AG(F,53P) ⊂ AG(F,55P) [i] based on
- linear OA(2515, 65, F25, 11) (dual of [65, 50, 12]-code), using algebraic-geometric code AG(F,53P) [i] based on function field F/F25 with g(F) = 4 and N(F) ≥ 66, using
- linear OA(2513, 65, F25, 9) (dual of [65, 52, 10]-code), using algebraic-geometric code AG(F,55P) [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,53P) ⊂ AG(F,55P) [i] based on
- linear OA(2543, 628, F25, 22) (dual of [628, 585, 23]-code), using
- construction XX applied to C1 = C([623,19]), C2 = C([0,20]), C3 = C1 + C2 = C([0,19]), and C∩ = C1 ∩ C2 = C([623,20]) [i] based on
- 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 = {−1,0,…,19}, and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(2541, 624, F25, 21) (dual of [624, 583, 22]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 624 = 252−1, defining interval I = [0,20], and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(2543, 624, F25, 22) (dual of [624, 581, 23]-code), using the primitive BCH-code C(I) with length 624 = 252−1, defining interval I = {−1,0,…,20}, and designed minimum distance d ≥ |I|+1 = 23 [i]
- linear OA(2539, 624, F25, 20) (dual of [624, 585, 21]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 624 = 252−1, defining interval I = [0,19], and designed minimum distance d ≥ |I|+1 = 21 [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([623,19]), C2 = C([0,20]), C3 = C1 + C2 = C([0,19]), and C∩ = C1 ∩ C2 = C([623,20]) [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(2559, 348, F25, 2, 22) (dual of [(348, 2), 637, 23]-NRT-code) | [i] | OOA Folding | |