Information on Result #1187698
Digital (214, 243, 299597)-net over F4, using net defined by OOA based on linear OOA(4243, 299597, F4, 29, 29) (dual of [(299597, 29), 8688070, 30]-NRT-code), using
- OOA 14-folding and stacking with additional row [i] based on linear OA(4243, 4194359, F4, 29) (dual of [4194359, 4194116, 30]-code), using
- 1 times code embedding in larger space [i] based on linear OA(4242, 4194358, F4, 29) (dual of [4194358, 4194116, 30]-code), using
- construction X applied to Ce(28) ⊂ Ce(22) [i] based on
- linear OA(4232, 4194304, F4, 29) (dual of [4194304, 4194072, 30]-code), using an extension Ce(28) of the primitive narrow-sense BCH-code C(I) with length 4194303 = 411−1, defining interval I = [1,28], and designed minimum distance d ≥ |I|+1 = 29 [i]
- linear OA(4188, 4194304, F4, 23) (dual of [4194304, 4194116, 24]-code), using an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 4194303 = 411−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [i]
- linear OA(410, 54, F4, 5) (dual of [54, 44, 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 Ce(28) ⊂ Ce(22) [i] based on
- 1 times code embedding in larger space [i] based on linear OA(4242, 4194358, F4, 29) (dual of [4194358, 4194116, 30]-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 (215, 243, 299597)-net over F4 | [i] | t-Expansion | |
| 2 | Digital (215, 244, 299597)-net over F4 | [i] | Net Duplication | |
| 3 | Digital (216, 245, 299597)-net over F4 | [i] | ||