Information on Result #2882474
Linear OOA(25659, 13108, F256, 5, 29) (dual of [(13108, 5), 65481, 30]-NRT-code), using 2561 times duplication based on linear OOA(25658, 13108, F256, 5, 29) (dual of [(13108, 5), 65482, 30]-NRT-code), using
- OOA 5-folding [i] based on linear OA(25658, 65540, F256, 29) (dual of [65540, 65482, 30]-code), using
- discarding factors / shortening the dual code based on linear OA(25658, 65542, F256, 29) (dual of [65542, 65484, 30]-code), using
- construction X applied to C([0,14]) ⊂ C([0,13]) [i] based on
- linear OA(25657, 65537, F256, 29) (dual of [65537, 65480, 30]-code), using the expurgated narrow-sense BCH-code C(I) with length 65537 | 2564−1, defining interval I = [0,14], and minimum distance d ≥ |{−14,−13,…,14}|+1 = 30 (BCH-bound) [i]
- linear OA(25653, 65537, F256, 27) (dual of [65537, 65484, 28]-code), using the expurgated narrow-sense BCH-code C(I) with length 65537 | 2564−1, defining interval I = [0,13], and minimum distance d ≥ |{−13,−12,…,13}|+1 = 28 (BCH-bound) [i]
- linear OA(2561, 5, F256, 1) (dual of [5, 4, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(2561, s, F256, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
- construction X applied to C([0,14]) ⊂ C([0,13]) [i] based on
- discarding factors / shortening the dual code based on linear OA(25658, 65542, F256, 29) (dual of [65542, 65484, 30]-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 OOA(25659, 13108, F256, 6, 29) (dual of [(13108, 6), 78589, 30]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Digital (30, 59, 13108)-net over F256 | [i] | ||