Information on Result #1203994
Digital (31, 54, 1492)-net over F128, using net defined by OOA based on linear OOA(12854, 1492, F128, 23, 23) (dual of [(1492, 23), 34262, 24]-NRT-code), using
- OOA 11-folding and stacking with additional row [i] based on linear OA(12854, 16413, F128, 23) (dual of [16413, 16359, 24]-code), using
- discarding factors / shortening the dual code based on linear OA(12854, 16414, F128, 23) (dual of [16414, 16360, 24]-code), using
- construction X applied to C([0,11]) ⊂ C([0,6]) [i] based on
- linear OA(12845, 16385, F128, 23) (dual of [16385, 16340, 24]-code), using the expurgated narrow-sense BCH-code C(I) with length 16385 | 1284−1, defining interval I = [0,11], and minimum distance d ≥ |{−11,−10,…,11}|+1 = 24 (BCH-bound) [i]
- linear OA(12825, 16385, F128, 13) (dual of [16385, 16360, 14]-code), using the expurgated narrow-sense BCH-code C(I) with length 16385 | 1284−1, defining interval I = [0,6], and minimum distance d ≥ |{−6,−5,…,6}|+1 = 14 (BCH-bound) [i]
- linear OA(1289, 29, F128, 9) (dual of [29, 20, 10]-code or 29-arc in PG(8,128)), using
- discarding factors / shortening the dual code based on linear OA(1289, 128, F128, 9) (dual of [128, 119, 10]-code or 128-arc in PG(8,128)), using
- Reed–Solomon code RS(119,128) [i]
- discarding factors / shortening the dual code based on linear OA(1289, 128, F128, 9) (dual of [128, 119, 10]-code or 128-arc in PG(8,128)), using
- construction X applied to C([0,11]) ⊂ C([0,6]) [i] based on
- discarding factors / shortening the dual code based on linear OA(12854, 16414, F128, 23) (dual of [16414, 16360, 24]-code), using
Mode: Constructive and 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 | Digital (32, 55, 1492)-net over F128 | [i] | Net Duplication | |
| 2 | Digital (31, 53, 1492)-net over F128 | [i] | m-Reduction | |
| 3 | (40, 63, 1492)-net in base 64 | [i] | Base Change | |