Information on Result #682941
Linear OA(5139, 3184, F5, 30) (dual of [3184, 3045, 31]-code), using construction X applied to C([0,15]) ⊂ C([0,10]) based on
- linear OA(5121, 3126, F5, 31) (dual of [3126, 3005, 32]-code), using the expurgated narrow-sense BCH-code C(I) with length 3126 | 510−1, defining interval I = [0,15], and minimum distance d ≥ |{−15,−14,…,15}|+1 = 32 (BCH-bound) [i]
- linear OA(581, 3126, F5, 21) (dual of [3126, 3045, 22]-code), using the expurgated narrow-sense BCH-code C(I) with length 3126 | 510−1, defining interval I = [0,10], and minimum distance d ≥ |{−10,−9,…,10}|+1 = 22 (BCH-bound) [i]
- linear OA(518, 58, F5, 8) (dual of [58, 40, 9]-code), using
- discarding factors / shortening the dual code based on linear OA(518, 62, F5, 8) (dual of [62, 44, 9]-code), using
- the cyclic code C(A) with length 62 | 53−1, defining set A = {2,3,8,9,11,12}, and minimum distance d ≥ |{8,9,…,15}|+1 = 9 (BCH-bound) [i]
- discarding factors / shortening the dual code based on linear OA(518, 62, F5, 8) (dual of [62, 44, 9]-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(5140, 3185, F5, 30) (dual of [3185, 3045, 31]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OOA(5139, 1592, F5, 2, 30) (dual of [(1592, 2), 3045, 31]-NRT-code) | [i] | OOA Folding | |
| 3 | Linear OOA(5139, 1061, F5, 3, 30) (dual of [(1061, 3), 3044, 31]-NRT-code) | [i] | ||