Information on Result #1638501
Linear OOA(2236, 2798931, F2, 5, 16) (dual of [(2798931, 5), 13994419, 17]-NRT-code), using embedding of OOA with Gilbert–Varšamov bound based on linear OOA(2236, 2798931, F2, 3, 16) (dual of [(2798931, 3), 8396557, 17]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(252, 2730, F2, 3, 8) (dual of [(2730, 3), 8138, 9]-NRT-code), using
- OOA 3-folding [i] based on linear OA(252, 8190, F2, 8) (dual of [8190, 8138, 9]-code), using
- discarding factors / shortening the dual code based on linear OA(252, 8192, F2, 8) (dual of [8192, 8140, 9]-code), using
- 1 times truncation [i] based on linear OA(253, 8193, F2, 9) (dual of [8193, 8140, 10]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 8193 | 226−1, 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(253, 8193, F2, 9) (dual of [8193, 8140, 10]-code), using
- discarding factors / shortening the dual code based on linear OA(252, 8192, F2, 8) (dual of [8192, 8140, 9]-code), using
- OOA 3-folding [i] based on linear OA(252, 8190, F2, 8) (dual of [8190, 8138, 9]-code), using
- linear OOA(2184, 2796201, F2, 3, 16) (dual of [(2796201, 3), 8388419, 17]-NRT-code), using
- OOA 3-folding [i] 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]
- OOA 3-folding [i] based on linear OA(2184, large, F2, 16) (dual of [large, large−184, 17]-code), using
- linear OOA(252, 2730, F2, 3, 8) (dual of [(2730, 3), 8138, 9]-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.