Information on Result #3209545
Digital (129, 153, 5464)-net over F4, using t-expansion based on digital (128, 153, 5464)-net over F4, using
- net defined by OOA [i] based on linear OOA(4153, 5464, F4, 25, 25) (dual of [(5464, 25), 136447, 26]-NRT-code), using
- OOA 12-folding and stacking with additional row [i] based on linear OA(4153, 65569, F4, 25) (dual of [65569, 65416, 26]-code), using
- discarding factors / shortening the dual code based on linear OA(4153, 65570, F4, 25) (dual of [65570, 65417, 26]-code), using
- construction XX applied to Ce(24) ⊂ Ce(20) ⊂ Ce(18) [i] based on
- linear OA(4145, 65536, F4, 25) (dual of [65536, 65391, 26]-code), using an extension Ce(24) of the primitive narrow-sense BCH-code C(I) with length 65535 = 48−1, defining interval I = [1,24], and designed minimum distance d ≥ |I|+1 = 25 [i]
- linear OA(4121, 65536, F4, 21) (dual of [65536, 65415, 22]-code), using an extension Ce(20) of the primitive narrow-sense BCH-code C(I) with length 65535 = 48−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [i]
- linear OA(4113, 65536, F4, 19) (dual of [65536, 65423, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 65535 = 48−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
- linear OA(45, 31, F4, 3) (dual of [31, 26, 4]-code or 31-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(41, 3, F4, 1) (dual of [3, 2, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(41, 4, F4, 1) (dual of [4, 3, 2]-code), using
- Reed–Solomon code RS(3,4) [i]
- discarding factors / shortening the dual code based on linear OA(41, 4, F4, 1) (dual of [4, 3, 2]-code), using
- construction XX applied to Ce(24) ⊂ Ce(20) ⊂ Ce(18) [i] based on
- discarding factors / shortening the dual code based on linear OA(4153, 65570, F4, 25) (dual of [65570, 65417, 26]-code), using
- OOA 12-folding and stacking with additional row [i] based on linear OA(4153, 65569, F4, 25) (dual of [65569, 65416, 26]-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 (130, 154, 5464)-net over F4 | [i] | Net Duplication | |