Information on Result #3267720
Digital (43, 64, 209716)-net over F128, using 1281 times duplication based on digital (42, 63, 209716)-net over F128, using
- net defined by OOA [i] based on linear OOA(12863, 209716, F128, 21, 21) (dual of [(209716, 21), 4403973, 22]-NRT-code), using
- OOA 10-folding and stacking with additional row [i] based on linear OA(12863, 2097161, F128, 21) (dual of [2097161, 2097098, 22]-code), using
- discarding factors / shortening the dual code based on linear OA(12863, 2097163, F128, 21) (dual of [2097163, 2097100, 22]-code), using
- construction X applied to Ce(20) ⊂ Ce(17) [i] based on
- linear OA(12861, 2097152, F128, 21) (dual of [2097152, 2097091, 22]-code), using an extension Ce(20) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 1283−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [i]
- linear OA(12852, 2097152, F128, 18) (dual of [2097152, 2097100, 19]-code), using an extension Ce(17) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 1283−1, defining interval I = [1,17], and designed minimum distance d ≥ |I|+1 = 18 [i]
- linear OA(1282, 11, F128, 2) (dual of [11, 9, 3]-code or 11-arc in PG(1,128)), using
- discarding factors / shortening the dual code based on linear OA(1282, 128, F128, 2) (dual of [128, 126, 3]-code or 128-arc in PG(1,128)), using
- Reed–Solomon code RS(126,128) [i]
- discarding factors / shortening the dual code based on linear OA(1282, 128, F128, 2) (dual of [128, 126, 3]-code or 128-arc in PG(1,128)), using
- construction X applied to Ce(20) ⊂ Ce(17) [i] based on
- discarding factors / shortening the dual code based on linear OA(12863, 2097163, F128, 21) (dual of [2097163, 2097100, 22]-code), using
- OOA 10-folding and stacking with additional row [i] based on linear OA(12863, 2097161, F128, 21) (dual of [2097161, 2097098, 22]-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 | (91, 112, 209716)-net in base 16 | [i] | Base Change | |