Information on Result #737209
Linear OA(4232, 65624, F4, 35) (dual of [65624, 65392, 36]-code), using construction X applied to C([0,17]) ⊂ C([0,12]) based on
- linear OA(4209, 65537, F4, 35) (dual of [65537, 65328, 36]-code), using the expurgated narrow-sense BCH-code C(I) with length 65537 | 416−1, defining interval I = [0,17], and minimum distance d ≥ |{−17,−16,…,17}|+1 = 36 (BCH-bound) [i]
- linear OA(4145, 65537, F4, 25) (dual of [65537, 65392, 26]-code), using the expurgated narrow-sense BCH-code C(I) with length 65537 | 416−1, defining interval I = [0,12], and minimum distance d ≥ |{−12,−11,…,12}|+1 = 26 (BCH-bound) [i]
- linear OA(423, 87, F4, 9) (dual of [87, 64, 10]-code), using
- discarding factors / shortening the dual code based on linear OA(423, 90, F4, 9) (dual of [90, 67, 10]-code), using
- construction X applied to C({2,5,6,14,17,21}) ⊂ C({2,5,6,14,17}) [i] based on
- linear OA(422, 85, F4, 9) (dual of [85, 63, 10]-code), using the cyclic code C(A) with length 85 | 44−1, defining set A = {2,5,6,14,17,21}, and minimum distance d ≥ |{−4,−1,2,…,20}|+1 = 10 (BCH-bound) [i]
- linear OA(418, 85, F4, 7) (dual of [85, 67, 8]-code), using the cyclic code C(A) with length 85 | 44−1, defining set A = {2,5,6,14,17}, and minimum distance d ≥ |{2,5,8,…,20}|+1 = 8 (BCH-bound) [i]
- linear OA(41, 5, F4, 1) (dual of [5, 4, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(41, s, F4, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
- construction X applied to C({2,5,6,14,17,21}) ⊂ C({2,5,6,14,17}) [i] based on
- discarding factors / shortening the dual code based on linear OA(423, 90, F4, 9) (dual of [90, 67, 10]-code), 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 OA(4233, 65625, F4, 35) (dual of [65625, 65392, 36]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OOA(4232, 32812, F4, 2, 35) (dual of [(32812, 2), 65392, 36]-NRT-code) | [i] | OOA Folding | |