Information on Result #1196064
Digital (43, 52, 2101058)-net over F25, using net defined by OOA based on linear OOA(2552, 2101058, F25, 10, 9) (dual of [(2101058, 10), 21010528, 10]-NRT-code), using
- OOA 2-folding and stacking with additional row [i] based on linear OOA(2552, 4202117, F25, 2, 9) (dual of [(4202117, 2), 8404182, 10]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(2511, 7816, F25, 2, 4) (dual of [(7816, 2), 15621, 5]-NRT-code), using
- OOA 2-folding [i] based on linear OA(2511, 15632, F25, 4) (dual of [15632, 15621, 5]-code), using
- construction X applied to Ce(3) ⊂ Ce(1) [i] based on
- linear OA(2510, 15625, F25, 4) (dual of [15625, 15615, 5]-code), using an extension Ce(3) of the primitive narrow-sense BCH-code C(I) with length 15624 = 253−1, defining interval I = [1,3], and designed minimum distance d ≥ |I|+1 = 4 [i]
- linear OA(254, 15625, F25, 2) (dual of [15625, 15621, 3]-code), using an extension Ce(1) of the primitive narrow-sense BCH-code C(I) with length 15624 = 253−1, defining interval I = [1,1], and designed minimum distance d ≥ |I|+1 = 2 [i]
- linear OA(251, 7, F25, 1) (dual of [7, 6, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(251, s, F25, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
- construction X applied to Ce(3) ⊂ Ce(1) [i] based on
- OOA 2-folding [i] based on linear OA(2511, 15632, F25, 4) (dual of [15632, 15621, 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(2511, 7816, F25, 2, 4) (dual of [(7816, 2), 15621, 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 (95, 104, 4202116)-net over F5 | [i] | Trace Code for Nets | |