Information on Result #678999
Linear OA(4157, 16443, F4, 27) (dual of [16443, 16286, 28]-code), using construction X applied to C([0,13]) ⊂ C([0,9]) based on
- linear OA(4141, 16385, F4, 27) (dual of [16385, 16244, 28]-code), using the expurgated narrow-sense BCH-code C(I) with length 16385 | 414−1, defining interval I = [0,13], and minimum distance d ≥ |{−13,−12,…,13}|+1 = 28 (BCH-bound) [i]
- linear OA(499, 16385, F4, 19) (dual of [16385, 16286, 20]-code), using the expurgated narrow-sense BCH-code C(I) with length 16385 | 414−1, defining interval I = [0,9], and minimum distance d ≥ |{−9,−8,…,9}|+1 = 20 (BCH-bound) [i]
- linear OA(416, 58, F4, 7) (dual of [58, 42, 8]-code), using
- discarding factors / shortening the dual code based on linear OA(416, 63, F4, 7) (dual of [63, 47, 8]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 63 = 43−1, defining interval I = [0,6], and designed minimum distance d ≥ |I|+1 = 8 [i]
- discarding factors / shortening the dual code based on linear OA(416, 63, F4, 7) (dual of [63, 47, 8]-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(4158, 16444, F4, 27) (dual of [16444, 16286, 28]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OA(4158, 16445, F4, 27) (dual of [16445, 16287, 28]-code) | [i] | Construction X with Varšamov Bound | |
| 3 | Linear OOA(4157, 8221, F4, 2, 27) (dual of [(8221, 2), 16285, 28]-NRT-code) | [i] | OOA Folding | |
| 4 | Linear OOA(4157, 5481, F4, 3, 27) (dual of [(5481, 3), 16286, 28]-NRT-code) | [i] | ||