Information on Result #1187086
Digital (155, 176, 419435)-net over F4, using net defined by OOA based on linear OOA(4176, 419435, F4, 21, 21) (dual of [(419435, 21), 8807959, 22]-NRT-code), using
- OOA 10-folding and stacking with additional row [i] based on linear OA(4176, 4194351, F4, 21) (dual of [4194351, 4194175, 22]-code), using
- discarding factors / shortening the dual code based on linear OA(4176, 4194358, F4, 21) (dual of [4194358, 4194182, 22]-code), using
- construction X applied to Ce(20) ⊂ Ce(14) [i] based on
- linear OA(4166, 4194304, F4, 21) (dual of [4194304, 4194138, 22]-code), using an extension Ce(20) of the primitive narrow-sense BCH-code C(I) with length 4194303 = 411−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [i]
- linear OA(4122, 4194304, F4, 15) (dual of [4194304, 4194182, 16]-code), using an extension Ce(14) of the primitive narrow-sense BCH-code C(I) with length 4194303 = 411−1, defining interval I = [1,14], and designed minimum distance d ≥ |I|+1 = 15 [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(20) ⊂ Ce(14) [i] based on
- discarding factors / shortening the dual code based on linear OA(4176, 4194358, F4, 21) (dual of [4194358, 4194182, 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 | Digital (155, 175, 419435)-net over F4 | [i] | m-Reduction | |