Information on Result #1688610
Linear OOA(2245, 1677891, F2, 7, 19) (dual of [(1677891, 7), 11744992, 20]-NRT-code), using embedding of OOA with Gilbert–Varšamov bound based on linear OOA(2245, 1677891, F2, 5, 19) (dual of [(1677891, 5), 8389210, 20]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(237, 171, F2, 5, 9) (dual of [(171, 5), 818, 10]-NRT-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(237, 171, F2, 3, 9) (dual of [(171, 3), 476, 10]-NRT-code), using
- OOA 3-folding [i] based on linear OA(237, 513, F2, 9) (dual of [513, 476, 10]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 513 | 218−1, defining interval I = [0,4], and minimum distance d ≥ |{−4,−3,…,4}|+1 = 10 (BCH-bound) [i]
- OOA 3-folding [i] based on linear OA(237, 513, F2, 9) (dual of [513, 476, 10]-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(237, 171, F2, 3, 9) (dual of [(171, 3), 476, 10]-NRT-code), using
- linear OOA(2208, 1677720, F2, 5, 19) (dual of [(1677720, 5), 8388392, 20]-NRT-code), using
- OOA 5-folding [i] based on linear OA(2208, 8388600, F2, 19) (dual of [8388600, 8388392, 20]-code), using
- discarding factors / shortening the dual code based on linear OA(2208, large, F2, 19) (dual of [large, large−208, 20]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 8388607 = 223−1, defining interval I = [0,18], and designed minimum distance d ≥ |I|+1 = 20 [i]
- discarding factors / shortening the dual code based on linear OA(2208, large, F2, 19) (dual of [large, large−208, 20]-code), using
- OOA 5-folding [i] based on linear OA(2208, 8388600, F2, 19) (dual of [8388600, 8388392, 20]-code), using
- linear OOA(237, 171, F2, 5, 9) (dual of [(171, 5), 818, 10]-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.