Information on Result #733561
Linear OA(2746, 19744, F27, 13) (dual of [19744, 19698, 14]-code), using (u, u+v)-construction based on
- linear OA(279, 58, F27, 6) (dual of [58, 49, 7]-code), using
- construction X applied to C([25,30]) ⊂ C([26,30]) [i] based on
- linear OA(279, 56, F27, 6) (dual of [56, 47, 7]-code), using the BCH-code C(I) with length 56 | 272−1, defining interval I = {25,26,…,30}, and designed minimum distance d ≥ |I|+1 = 7 [i]
- linear OA(277, 56, F27, 5) (dual of [56, 49, 6]-code), using the BCH-code C(I) with length 56 | 272−1, defining interval I = {26,27,28,29,30}, and designed minimum distance d ≥ |I|+1 = 6 [i]
- 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 X applied to C([25,30]) ⊂ C([26,30]) [i] based on
- linear OA(2737, 19686, F27, 13) (dual of [19686, 19649, 14]-code), using
- construction X applied to Ce(12) ⊂ Ce(11) [i] based on
- linear OA(2737, 19683, F27, 13) (dual of [19683, 19646, 14]-code), using an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 19682 = 273−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
- linear OA(2734, 19683, F27, 12) (dual of [19683, 19649, 13]-code), using an extension Ce(11) of the primitive narrow-sense BCH-code C(I) with length 19682 = 273−1, defining interval I = [1,11], and designed minimum distance d ≥ |I|+1 = 12 [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(12) ⊂ Ce(11) [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(2746, 9872, F27, 2, 13) (dual of [(9872, 2), 19698, 14]-NRT-code) | [i] | OOA Folding | |