Information on Result #2882485
Linear OOA(25667, 13108, F256, 5, 33) (dual of [(13108, 5), 65473, 34]-NRT-code), using 2561 times duplication based on linear OOA(25666, 13108, F256, 5, 33) (dual of [(13108, 5), 65474, 34]-NRT-code), using
- OOA 5-folding [i] based on linear OA(25666, 65540, F256, 33) (dual of [65540, 65474, 34]-code), using
- discarding factors / shortening the dual code based on linear OA(25666, 65542, F256, 33) (dual of [65542, 65476, 34]-code), using
- construction X applied to C([0,16]) ⊂ C([0,15]) [i] based on
- linear OA(25665, 65537, F256, 33) (dual of [65537, 65472, 34]-code), using the expurgated narrow-sense BCH-code C(I) with length 65537 | 2564−1, defining interval I = [0,16], and minimum distance d ≥ |{−16,−15,…,16}|+1 = 34 (BCH-bound) [i]
- linear OA(25661, 65537, F256, 31) (dual of [65537, 65476, 32]-code), using the expurgated narrow-sense BCH-code C(I) with length 65537 | 2564−1, defining interval I = [0,15], and minimum distance d ≥ |{−15,−14,…,15}|+1 = 32 (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([0,16]) ⊂ C([0,15]) [i] based on
- discarding factors / shortening the dual code based on linear OA(25666, 65542, F256, 33) (dual of [65542, 65476, 34]-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(25667, 13108, F256, 6, 33) (dual of [(13108, 6), 78581, 34]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Digital (34, 67, 13108)-net over F256 | [i] | ||