Information on Result #1709832
Digital (196, 212, 2097213)-net over F2, using net defined by OOA based on linear OOA(2212, 2097213, F2, 24, 16) (dual of [(2097213, 24), 50332900, 17]-NRT-code), using
- OOA stacking with additional row [i] based on linear OOA(2212, 2097214, F2, 8, 16) (dual of [(2097214, 8), 16777500, 17]-NRT-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(2212, 2097214, F2, 4, 16) (dual of [(2097214, 4), 8388644, 17]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(228, 64, F2, 4, 8) (dual of [(64, 4), 228, 9]-NRT-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(228, 64, F2, 2, 8) (dual of [(64, 2), 100, 9]-NRT-code), using
- OOA 2-folding [i] based on linear OA(228, 128, F2, 8) (dual of [128, 100, 9]-code), using
- 1 times truncation [i] based on linear OA(229, 129, F2, 9) (dual of [129, 100, 10]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 129 | 214−1, defining interval I = [0,4], and minimum distance d ≥ |{−4,−3,…,4}|+1 = 10 (BCH-bound) [i]
- 1 times truncation [i] based on linear OA(229, 129, F2, 9) (dual of [129, 100, 10]-code), using
- OOA 2-folding [i] based on linear OA(228, 128, F2, 8) (dual of [128, 100, 9]-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(228, 64, F2, 2, 8) (dual of [(64, 2), 100, 9]-NRT-code), using
- linear OOA(2184, 2097150, F2, 4, 16) (dual of [(2097150, 4), 8388416, 17]-NRT-code), using
- OOA 4-folding [i] based on linear OA(2184, 8388600, F2, 16) (dual of [8388600, 8388416, 17]-code), using
- discarding factors / shortening the dual code based on linear OA(2184, large, F2, 16) (dual of [large, large−184, 17]-code), using
- the primitive narrow-sense BCH-code C(I) with length 8388607 = 223−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
- discarding factors / shortening the dual code based on linear OA(2184, large, F2, 16) (dual of [large, large−184, 17]-code), using
- OOA 4-folding [i] based on linear OA(2184, 8388600, F2, 16) (dual of [8388600, 8388416, 17]-code), using
- linear OOA(228, 64, F2, 4, 8) (dual of [(64, 4), 228, 9]-NRT-code), using
- (u, u+v)-construction [i] based on
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(2212, 2097214, F2, 4, 16) (dual of [(2097214, 4), 8388644, 17]-NRT-code), using
Mode: 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.