Information on Result #1196314
Digital (59, 72, 1398204)-net over F25, using net defined by OOA based on linear OOA(2572, 1398204, F25, 14, 13) (dual of [(1398204, 14), 19574784, 14]-NRT-code), using
- OOA 3-folding and stacking with additional row [i] based on linear OOA(2572, 4194613, F25, 2, 13) (dual of [(4194613, 2), 8389154, 14]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(2572, 4194615, F25, 2, 13) (dual of [(4194615, 2), 8389158, 14]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(2511, 314, F25, 2, 6) (dual of [(314, 2), 617, 7]-NRT-code), using
- OOA 2-folding [i] based on linear OA(2511, 628, F25, 6) (dual of [628, 617, 7]-code), using
- construction XX applied to C1 = C([623,3]), C2 = C([0,4]), C3 = C1 + C2 = C([0,3]), and C∩ = C1 ∩ C2 = C([623,4]) [i] based on
- linear OA(259, 624, F25, 5) (dual of [624, 615, 6]-code), using the primitive BCH-code C(I) with length 624 = 252−1, defining interval I = {−1,0,1,2,3}, and designed minimum distance d ≥ |I|+1 = 6 [i]
- linear OA(259, 624, F25, 5) (dual of [624, 615, 6]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 624 = 252−1, defining interval I = [0,4], and designed minimum distance d ≥ |I|+1 = 6 [i]
- linear OA(2511, 624, F25, 6) (dual of [624, 613, 7]-code), using the primitive BCH-code C(I) with length 624 = 252−1, defining interval I = {−1,0,…,4}, and designed minimum distance d ≥ |I|+1 = 7 [i]
- linear OA(257, 624, F25, 4) (dual of [624, 617, 5]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 624 = 252−1, defining interval I = [0,3], and designed minimum distance d ≥ |I|+1 = 5 [i]
- linear OA(250, 2, F25, 0) (dual of [2, 2, 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
- linear OA(250, 2, F25, 0) (dual of [2, 2, 1]-code) (see above)
- construction XX applied to C1 = C([623,3]), C2 = C([0,4]), C3 = C1 + C2 = C([0,3]), and C∩ = C1 ∩ C2 = C([623,4]) [i] based on
- OOA 2-folding [i] based on linear OA(2511, 628, F25, 6) (dual of [628, 617, 7]-code), using
- linear OOA(2561, 4194301, F25, 2, 13) (dual of [(4194301, 2), 8388541, 14]-NRT-code), using
- OOA 2-folding [i] based on linear OA(2561, 8388602, F25, 13) (dual of [8388602, 8388541, 14]-code), using
- discarding factors / shortening the dual code based on linear OA(2561, large, F25, 13) (dual of [large, large−61, 14]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 9765626 | 2510−1, defining interval I = [0,6], and minimum distance d ≥ |{−6,−5,…,6}|+1 = 14 (BCH-bound) [i]
- discarding factors / shortening the dual code based on linear OA(2561, large, F25, 13) (dual of [large, large−61, 14]-code), using
- OOA 2-folding [i] based on linear OA(2561, 8388602, F25, 13) (dual of [8388602, 8388541, 14]-code), using
- linear OOA(2511, 314, F25, 2, 6) (dual of [(314, 2), 617, 7]-NRT-code), using
- (u, u+v)-construction [i] based on
- discarding factors / shortening the dual code based on linear OOA(2572, 4194615, F25, 2, 13) (dual of [(4194615, 2), 8389158, 14]-NRT-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 (131, 144, 2796408)-net over F5 | [i] | Trace Code for Nets | |