Information on Result #1633558
Linear OOA(2162, 2097278, F2, 5, 13) (dual of [(2097278, 5), 10486228, 14]-NRT-code), using embedding of OOA with Gilbert–Varšamov bound based on linear OOA(2162, 2097278, F2, 4, 13) (dual of [(2097278, 4), 8388950, 14]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(221, 127, F2, 4, 6) (dual of [(127, 4), 487, 7]-NRT-code), using
- extracting embedded OOA [i] based on digital (15, 21, 127)-net over F2, using
- linear OOA(2141, 2097151, F2, 4, 13) (dual of [(2097151, 4), 8388463, 14]-NRT-code), using
- OOA 2-folding [i] based on linear OOA(2141, 4194302, F2, 2, 13) (dual of [(4194302, 2), 8388463, 14]-NRT-code), using
- 1 times NRT-code embedding in larger space [i] based on linear OOA(2139, 4194301, F2, 2, 13) (dual of [(4194301, 2), 8388463, 14]-NRT-code), using
- OOA 2-folding [i] based on linear OA(2139, 8388602, F2, 13) (dual of [8388602, 8388463, 14]-code), using
- discarding factors / shortening the dual code based on linear OA(2139, large, F2, 13) (dual of [large, large−139, 14]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 8388609 | 246−1, 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(2139, large, F2, 13) (dual of [large, large−139, 14]-code), using
- OOA 2-folding [i] based on linear OA(2139, 8388602, F2, 13) (dual of [8388602, 8388463, 14]-code), using
- 1 times NRT-code embedding in larger space [i] based on linear OOA(2139, 4194301, F2, 2, 13) (dual of [(4194301, 2), 8388463, 14]-NRT-code), using
- OOA 2-folding [i] based on linear OOA(2141, 4194302, F2, 2, 13) (dual of [(4194302, 2), 8388463, 14]-NRT-code), using
- linear OOA(221, 127, F2, 4, 6) (dual of [(127, 4), 487, 7]-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.
Other Results with Identical Parameters
None.
Depending Results
None.