Information on Result #727307
Linear OA(27105, 735, F27, 54) (dual of [735, 630, 55]-code), using construction XX applied to C1 = C([726,50]), C2 = C([0,51]), C3 = C1 + C2 = C([0,50]), and C∩ = C1 ∩ C2 = C([726,51]) based on
- linear OA(27102, 728, F27, 53) (dual of [728, 626, 54]-code), using the primitive BCH-code C(I) with length 728 = 272−1, defining interval I = {−2,−1,…,50}, and designed minimum distance d ≥ |I|+1 = 54 [i]
- linear OA(27100, 728, F27, 52) (dual of [728, 628, 53]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 728 = 272−1, defining interval I = [0,51], and designed minimum distance d ≥ |I|+1 = 53 [i]
- linear OA(27104, 728, F27, 54) (dual of [728, 624, 55]-code), using the primitive BCH-code C(I) with length 728 = 272−1, defining interval I = {−2,−1,…,51}, and designed minimum distance d ≥ |I|+1 = 55 [i]
- linear OA(2798, 728, F27, 51) (dual of [728, 630, 52]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 728 = 272−1, defining interval I = [0,50], and designed minimum distance d ≥ |I|+1 = 52 [i]
- linear OA(271, 5, F27, 1) (dual of [5, 4, 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
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(27105, 367, F27, 2, 54) (dual of [(367, 2), 629, 55]-NRT-code) | [i] | OOA Folding | |