Information on Result #3221032
Digital (213, 253, 3279)-net over F4, using t-expansion based on digital (212, 253, 3279)-net over F4, using
- net defined by OOA [i] based on linear OOA(4253, 3279, F4, 41, 41) (dual of [(3279, 41), 134186, 42]-NRT-code), using
- OOA 20-folding and stacking with additional row [i] based on linear OA(4253, 65581, F4, 41) (dual of [65581, 65328, 42]-code), using
- 2 times code embedding in larger space [i] based on linear OA(4251, 65579, F4, 41) (dual of [65579, 65328, 42]-code), using
- construction X applied to C([0,20]) ⊂ C([0,17]) [i] based on
- linear OA(4241, 65537, F4, 41) (dual of [65537, 65296, 42]-code), using the expurgated narrow-sense BCH-code C(I) with length 65537 | 416−1, defining interval I = [0,20], and minimum distance d ≥ |{−20,−19,…,20}|+1 = 42 (BCH-bound) [i]
- linear OA(4209, 65537, F4, 35) (dual of [65537, 65328, 36]-code), using the expurgated narrow-sense BCH-code C(I) with length 65537 | 416−1, defining interval I = [0,17], and minimum distance d ≥ |{−17,−16,…,17}|+1 = 36 (BCH-bound) [i]
- linear OA(410, 42, F4, 5) (dual of [42, 32, 6]-code), using
- discarding factors / shortening the dual code based on linear OA(410, 63, F4, 5) (dual of [63, 53, 6]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 63 = 43−1, defining interval I = [0,3], and designed minimum distance d ≥ |I|+1 = 6 [i]
- discarding factors / shortening the dual code based on linear OA(410, 63, F4, 5) (dual of [63, 53, 6]-code), using
- construction X applied to C([0,20]) ⊂ C([0,17]) [i] based on
- 2 times code embedding in larger space [i] based on linear OA(4251, 65579, F4, 41) (dual of [65579, 65328, 42]-code), using
- OOA 20-folding and stacking with additional row [i] based on linear OA(4253, 65581, F4, 41) (dual of [65581, 65328, 42]-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 (214, 254, 3279)-net over F4 | [i] | Net Duplication | |
| 2 | Digital (215, 255, 3279)-net over F4 | [i] | ||