Information on Result #733242
Linear OA(27107, 19796, F27, 29) (dual of [19796, 19689, 30]-code), using (u, u+v)-construction based on
- linear OA(2725, 110, F27, 14) (dual of [110, 85, 15]-code), using
- construction XX applied to C1 = C([0,12]), C2 = C([2,13]), C3 = C1 + C2 = C([2,12]), and C∩ = C1 ∩ C2 = C([0,13]) [i] based on
- linear OA(2722, 104, F27, 13) (dual of [104, 82, 14]-code), using the expurgated narrow-sense BCH-code C(I) with length 104 | 272−1, defining interval I = [0,12], and designed minimum distance d ≥ |I|+1 = 14 [i]
- linear OA(2721, 104, F27, 12) (dual of [104, 83, 13]-code), using the BCH-code C(I) with length 104 | 272−1, defining interval I = {2,3,…,13}, and designed minimum distance d ≥ |I|+1 = 13 [i]
- linear OA(2724, 104, F27, 14) (dual of [104, 80, 15]-code), using the expurgated narrow-sense BCH-code C(I) with length 104 | 272−1, defining interval I = [0,13], and designed minimum distance d ≥ |I|+1 = 15 [i]
- linear OA(2719, 104, F27, 11) (dual of [104, 85, 12]-code), using the BCH-code C(I) with length 104 | 272−1, defining interval I = {2,3,…,12}, and designed minimum distance d ≥ |I|+1 = 12 [i]
- linear OA(271, 4, F27, 1) (dual of [4, 3, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(271, 27, F27, 1) (dual of [27, 26, 2]-code), using
- Reed–Solomon code RS(26,27) [i]
- discarding factors / shortening the dual code based on linear OA(271, 27, F27, 1) (dual of [27, 26, 2]-code), using
- linear OA(270, 2, F27, 0) (dual of [2, 2, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(270, s, F27, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
- construction XX applied to C1 = C([0,12]), C2 = C([2,13]), C3 = C1 + C2 = C([2,12]), and C∩ = C1 ∩ C2 = C([0,13]) [i] based on
- linear OA(2782, 19686, F27, 29) (dual of [19686, 19604, 30]-code), using
- construction X applied to Ce(28) ⊂ Ce(27) [i] based on
- linear OA(2782, 19683, F27, 29) (dual of [19683, 19601, 30]-code), using an extension Ce(28) of the primitive narrow-sense BCH-code C(I) with length 19682 = 273−1, defining interval I = [1,28], and designed minimum distance d ≥ |I|+1 = 29 [i]
- linear OA(2779, 19683, F27, 28) (dual of [19683, 19604, 29]-code), using an extension Ce(27) of the primitive narrow-sense BCH-code C(I) with length 19682 = 273−1, defining interval I = [1,27], and designed minimum distance d ≥ |I|+1 = 28 [i]
- linear OA(270, 3, F27, 0) (dual of [3, 3, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(270, s, F27, 0) (dual of [s, s, 1]-code) for arbitrarily large s (see above)
- construction X applied to Ce(28) ⊂ Ce(27) [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(27107, 9898, F27, 2, 29) (dual of [(9898, 2), 19689, 30]-NRT-code) | [i] | OOA Folding | |