Information on Result #1681433
Linear OOA(2139, 22794, F2, 7, 17) (dual of [(22794, 7), 159419, 18]-NRT-code), using embedding of OOA with Gilbert–Varšamov bound based on linear OOA(2139, 22794, F2, 5, 17) (dual of [(22794, 5), 113831, 18]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(2139, 26218, F2, 5, 17) (dual of [(26218, 5), 130951, 18]-NRT-code), using
- 21 times duplication [i] based on linear OOA(2138, 26218, F2, 5, 17) (dual of [(26218, 5), 130952, 18]-NRT-code), using
- OOA 5-folding [i] based on linear OA(2138, 131090, F2, 17) (dual of [131090, 130952, 18]-code), using
- construction X applied to Ce(16) ⊂ Ce(14) [i] based on
- linear OA(2137, 131072, F2, 17) (dual of [131072, 130935, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 131071 = 217−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
- linear OA(2120, 131072, F2, 15) (dual of [131072, 130952, 16]-code), using an extension Ce(14) of the primitive narrow-sense BCH-code C(I) with length 131071 = 217−1, defining interval I = [1,14], and designed minimum distance d ≥ |I|+1 = 15 [i]
- linear OA(21, 18, F2, 1) (dual of [18, 17, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(21, s, F2, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
- construction X applied to Ce(16) ⊂ Ce(14) [i] based on
- OOA 5-folding [i] based on linear OA(2138, 131090, F2, 17) (dual of [131090, 130952, 18]-code), using
- 21 times duplication [i] based on linear OOA(2138, 26218, F2, 5, 17) (dual of [(26218, 5), 130952, 18]-NRT-code), using
Mode: Linear.
Optimality
Show details for fixed k and m, n and k, k and s, k and t, n and m, m and s, m and t, n and s, n and t.
Other Results with Identical Parameters
None.
Depending Results
None.