Information on Result #2479174
Linear OOA(2203, 32789, F2, 2, 24) (dual of [(32789, 2), 65375, 25]-NRT-code), using 21 times duplication based on linear OOA(2202, 32789, F2, 2, 24) (dual of [(32789, 2), 65376, 25]-NRT-code), using
- 1 times NRT-code embedding in larger space [i] based on linear OOA(2200, 32788, F2, 2, 24) (dual of [(32788, 2), 65376, 25]-NRT-code), using
- OOA 2-folding [i] based on linear OA(2200, 65576, F2, 24) (dual of [65576, 65376, 25]-code), using
- strength reduction [i] based on linear OA(2200, 65576, F2, 25) (dual of [65576, 65376, 26]-code), using
- construction X applied to C([0,12]) ⊂ C([0,10]) [i] based on
- linear OA(2193, 65537, F2, 25) (dual of [65537, 65344, 26]-code), using the expurgated narrow-sense BCH-code C(I) with length 65537 | 232−1, defining interval I = [0,12], and minimum distance d ≥ |{−12,−11,…,12}|+1 = 26 (BCH-bound) [i]
- linear OA(2161, 65537, F2, 21) (dual of [65537, 65376, 22]-code), using the expurgated narrow-sense BCH-code C(I) with length 65537 | 232−1, defining interval I = [0,10], and minimum distance d ≥ |{−10,−9,…,10}|+1 = 22 (BCH-bound) [i]
- linear OA(27, 39, F2, 3) (dual of [39, 32, 4]-code or 39-cap in PG(6,2)), using
- discarding factors / shortening the dual code based on linear OA(27, 63, F2, 3) (dual of [63, 56, 4]-code or 63-cap in PG(6,2)), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 63 = 26−1, defining interval I = [0,1], and designed minimum distance d ≥ |I|+1 = 4 [i]
- discarding factors / shortening the dual code based on linear OA(27, 63, F2, 3) (dual of [63, 56, 4]-code or 63-cap in PG(6,2)), using
- construction X applied to C([0,12]) ⊂ C([0,10]) [i] based on
- strength reduction [i] based on linear OA(2200, 65576, F2, 25) (dual of [65576, 65376, 26]-code), using
- OOA 2-folding [i] based on linear OA(2200, 65576, F2, 24) (dual of [65576, 65376, 25]-code), using
Mode: Constructive and 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.