Information on Result #3212475
Digital (162, 186, 87384)-net over F4, using t-expansion based on digital (161, 186, 87384)-net over F4, using
- net defined by OOA [i] based on linear OOA(4186, 87384, F4, 25, 25) (dual of [(87384, 25), 2184414, 26]-NRT-code), using
- OOA 12-folding and stacking with additional row [i] based on linear OA(4186, 1048609, F4, 25) (dual of [1048609, 1048423, 26]-code), using
- discarding factors / shortening the dual code based on linear OA(4186, 1048611, F4, 25) (dual of [1048611, 1048425, 26]-code), using
- construction X applied to Ce(24) ⊂ Ce(20) [i] based on
- linear OA(4181, 1048576, F4, 25) (dual of [1048576, 1048395, 26]-code), using an extension Ce(24) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 410−1, defining interval I = [1,24], and designed minimum distance d ≥ |I|+1 = 25 [i]
- linear OA(4151, 1048576, F4, 21) (dual of [1048576, 1048425, 22]-code), using an extension Ce(20) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 410−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [i]
- linear OA(45, 35, F4, 3) (dual of [35, 30, 4]-code or 35-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
- construction X applied to Ce(24) ⊂ Ce(20) [i] based on
- discarding factors / shortening the dual code based on linear OA(4186, 1048611, F4, 25) (dual of [1048611, 1048425, 26]-code), using
- OOA 12-folding and stacking with additional row [i] based on linear OA(4186, 1048609, F4, 25) (dual of [1048609, 1048423, 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 (163, 187, 87384)-net over F4 | [i] | Net Duplication | |