Information on Result #1196068
Digital (45, 54, 2194807)-net over F25, using net defined by OOA based on linear OOA(2554, 2194807, F25, 10, 9) (dual of [(2194807, 10), 21948016, 10]-NRT-code), using
- OOA 2-folding and stacking with additional row [i] based on linear OOA(2554, 4389615, F25, 2, 9) (dual of [(4389615, 2), 8779176, 10]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(2513, 195314, F25, 2, 4) (dual of [(195314, 2), 390615, 5]-NRT-code), using
- OOA 2-folding [i] based on linear OA(2513, 390628, F25, 4) (dual of [390628, 390615, 5]-code), using
- discarding factors / shortening the dual code based on linear OA(2513, 390629, F25, 4) (dual of [390629, 390616, 5]-code), using
- construction X applied to Ce(3) ⊂ Ce(2) [i] based on
- linear OA(2513, 390625, F25, 4) (dual of [390625, 390612, 5]-code), using an extension Ce(3) of the primitive narrow-sense BCH-code C(I) with length 390624 = 254−1, defining interval I = [1,3], and designed minimum distance d ≥ |I|+1 = 4 [i]
- linear OA(259, 390625, F25, 3) (dual of [390625, 390616, 4]-code or 390625-cap in PG(8,25)), using an extension Ce(2) of the primitive narrow-sense BCH-code C(I) with length 390624 = 254−1, defining interval I = [1,2], and designed minimum distance d ≥ |I|+1 = 3 [i]
- linear OA(250, 4, F25, 0) (dual of [4, 4, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(250, s, F25, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
- construction X applied to Ce(3) ⊂ Ce(2) [i] based on
- discarding factors / shortening the dual code based on linear OA(2513, 390629, F25, 4) (dual of [390629, 390616, 5]-code), using
- OOA 2-folding [i] based on linear OA(2513, 390628, F25, 4) (dual of [390628, 390615, 5]-code), using
- linear OOA(2541, 4194301, F25, 2, 9) (dual of [(4194301, 2), 8388561, 10]-NRT-code), using
- OOA 2-folding [i] based on linear OA(2541, 8388602, F25, 9) (dual of [8388602, 8388561, 10]-code), using
- discarding factors / shortening the dual code based on linear OA(2541, large, F25, 9) (dual of [large, large−41, 10]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 9765626 | 2510−1, defining interval I = [0,4], and minimum distance d ≥ |{−4,−3,…,4}|+1 = 10 (BCH-bound) [i]
- discarding factors / shortening the dual code based on linear OA(2541, large, F25, 9) (dual of [large, large−41, 10]-code), using
- OOA 2-folding [i] based on linear OA(2541, 8388602, F25, 9) (dual of [8388602, 8388561, 10]-code), using
- linear OOA(2513, 195314, F25, 2, 4) (dual of [(195314, 2), 390615, 5]-NRT-code), using
- (u, u+v)-construction [i] based on
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 (99, 108, 4389614)-net over F5 | [i] | Trace Code for Nets | |