Information on Result #1187776
Digital (160, 191, 4371)-net over F4, using net defined by OOA based on linear OOA(4191, 4371, F4, 31, 31) (dual of [(4371, 31), 135310, 32]-NRT-code), using
- OOA 15-folding and stacking with additional row [i] based on linear OA(4191, 65566, F4, 31) (dual of [65566, 65375, 32]-code), using
- discarding factors / shortening the dual code based on linear OA(4191, 65567, F4, 31) (dual of [65567, 65376, 32]-code), using
- construction XX applied to Ce(30) ⊂ Ce(26) ⊂ Ce(25) [i] based on
- linear OA(4185, 65536, F4, 31) (dual of [65536, 65351, 32]-code), using an extension Ce(30) of the primitive narrow-sense BCH-code C(I) with length 65535 = 48−1, defining interval I = [1,30], and designed minimum distance d ≥ |I|+1 = 31 [i]
- linear OA(4161, 65536, F4, 27) (dual of [65536, 65375, 28]-code), using an extension Ce(26) of the primitive narrow-sense BCH-code C(I) with length 65535 = 48−1, defining interval I = [1,26], and designed minimum distance d ≥ |I|+1 = 27 [i]
- linear OA(4153, 65536, F4, 26) (dual of [65536, 65383, 27]-code), using an extension Ce(25) of the primitive narrow-sense BCH-code C(I) with length 65535 = 48−1, defining interval I = [1,25], and designed minimum distance d ≥ |I|+1 = 26 [i]
- linear OA(45, 30, F4, 3) (dual of [30, 25, 4]-code or 30-cap in PG(4,4)), using
- discarding factors / shortening the dual code based on linear OA(45, 41, F4, 3) (dual of [41, 36, 4]-code or 41-cap in PG(4,4)), using
- linear OA(40, 1, F4, 0) (dual of [1, 1, 1]-code), using
- dual of repetition code with length 1 [i]
- construction XX applied to Ce(30) ⊂ Ce(26) ⊂ Ce(25) [i] based on
- discarding factors / shortening the dual code based on linear OA(4191, 65567, F4, 31) (dual of [65567, 65376, 32]-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 (161, 192, 4371)-net over F4 | [i] | Net Duplication | |
| 2 | Digital (162, 193, 4371)-net over F4 | [i] | ||
| 3 | Digital (163, 194, 4371)-net over F4 | [i] | ||