Information on Result #1814553
Digital (21, 42, 13975)-net over F256, using embedding of OOA with Gilbert–Varšamov bound based on linear OOA(25642, 13975, F256, 4, 21) (dual of [(13975, 4), 55858, 22]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(25642, 16385, F256, 4, 21) (dual of [(16385, 4), 65498, 22]-NRT-code), using
- OOA 4-folding [i] based on linear OA(25642, 65540, F256, 21) (dual of [65540, 65498, 22]-code), using
- discarding factors / shortening the dual code based on linear OA(25642, 65542, F256, 21) (dual of [65542, 65500, 22]-code), using
- construction X applied to C([0,10]) ⊂ C([0,9]) [i] based on
- linear OA(25641, 65537, F256, 21) (dual of [65537, 65496, 22]-code), using the expurgated narrow-sense BCH-code C(I) with length 65537 | 2564−1, defining interval I = [0,10], and minimum distance d ≥ |{−10,−9,…,10}|+1 = 22 (BCH-bound) [i]
- linear OA(25637, 65537, F256, 19) (dual of [65537, 65500, 20]-code), using the expurgated narrow-sense BCH-code C(I) with length 65537 | 2564−1, defining interval I = [0,9], and minimum distance d ≥ |{−9,−8,…,9}|+1 = 20 (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([0,10]) ⊂ C([0,9]) [i] based on
- discarding factors / shortening the dual code based on linear OA(25642, 65542, F256, 21) (dual of [65542, 65500, 22]-code), using
- OOA 4-folding [i] based on linear OA(25642, 65540, F256, 21) (dual of [65540, 65498, 22]-code), using
Mode: Linear.
Optimality
Show details for fixed k and m, k and s, k and t, m and s, m and t, t and s.
Other Results with Identical Parameters
None.
Depending Results
The following results depend on this result:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | (27, 48, 13975)-net in base 128 | [i] | Base Change | |