Information on Result #1202532
Digital (67, 82, 2097150)-net over F81, using net defined by OOA based on linear OOA(8182, 2097150, F81, 18, 15) (dual of [(2097150, 18), 37748618, 16]-NRT-code), using
- OOA 4-folding and stacking with additional row [i] based on linear OOA(8182, 8388601, F81, 2, 15) (dual of [(8388601, 2), 16777120, 16]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(8182, 8388602, F81, 2, 15) (dual of [(8388602, 2), 16777122, 16]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(8125, 4194301, F81, 2, 7) (dual of [(4194301, 2), 8388577, 8]-NRT-code), using
- OOA 2-folding [i] based on linear OA(8125, 8388602, F81, 7) (dual of [8388602, 8388577, 8]-code), using
- discarding factors / shortening the dual code based on linear OA(8125, large, F81, 7) (dual of [large, large−25, 8]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 21523361 | 818−1, defining interval I = [0,3], and minimum distance d ≥ |{−3,−2,…,3}|+1 = 8 (BCH-bound) [i]
- discarding factors / shortening the dual code based on linear OA(8125, large, F81, 7) (dual of [large, large−25, 8]-code), using
- OOA 2-folding [i] based on linear OA(8125, 8388602, F81, 7) (dual of [8388602, 8388577, 8]-code), using
- linear OOA(8157, 4194301, F81, 2, 15) (dual of [(4194301, 2), 8388545, 16]-NRT-code), using
- OOA 2-folding [i] based on linear OA(8157, 8388602, F81, 15) (dual of [8388602, 8388545, 16]-code), using
- discarding factors / shortening the dual code based on linear OA(8157, large, F81, 15) (dual of [large, large−57, 16]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 21523361 | 818−1, defining interval I = [0,7], and minimum distance d ≥ |{−7,−6,…,7}|+1 = 16 (BCH-bound) [i]
- discarding factors / shortening the dual code based on linear OA(8157, large, F81, 15) (dual of [large, large−57, 16]-code), using
- OOA 2-folding [i] based on linear OA(8157, 8388602, F81, 15) (dual of [8388602, 8388545, 16]-code), using
- linear OOA(8125, 4194301, F81, 2, 7) (dual of [(4194301, 2), 8388577, 8]-NRT-code), using
- (u, u+v)-construction [i] based on
- discarding factors / shortening the dual code based on linear OOA(8182, 8388602, F81, 2, 15) (dual of [(8388602, 2), 16777122, 16]-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
None.