Information on Result #1674829
Linear OOA(2177, 362, F2, 7, 32) (dual of [(362, 7), 2357, 33]-NRT-code), using OOA 2-folding based on linear OOA(2177, 724, F2, 4, 32) (dual of [(724, 4), 2719, 33]-NRT-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(2177, 724, F2, 2, 32) (dual of [(724, 2), 1271, 33]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(2177, 1029, F2, 2, 32) (dual of [(1029, 2), 1881, 33]-NRT-code), using
- OOA 2-folding [i] based on linear OA(2177, 2058, F2, 32) (dual of [2058, 1881, 33]-code), using
- discarding factors / shortening the dual code based on linear OA(2177, 2059, F2, 32) (dual of [2059, 1882, 33]-code), using
- 1 times truncation [i] based on linear OA(2178, 2060, F2, 33) (dual of [2060, 1882, 34]-code), using
- construction X applied to Ce(32) ⊂ Ce(30) [i] based on
- linear OA(2177, 2048, F2, 33) (dual of [2048, 1871, 34]-code), using an extension Ce(32) of the primitive narrow-sense BCH-code C(I) with length 2047 = 211−1, defining interval I = [1,32], and designed minimum distance d ≥ |I|+1 = 33 [i]
- linear OA(2166, 2048, F2, 31) (dual of [2048, 1882, 32]-code), using an extension Ce(30) of the primitive narrow-sense BCH-code C(I) with length 2047 = 211−1, defining interval I = [1,30], and designed minimum distance d ≥ |I|+1 = 31 [i]
- linear OA(21, 12, F2, 1) (dual of [12, 11, 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(32) ⊂ Ce(30) [i] based on
- 1 times truncation [i] based on linear OA(2178, 2060, F2, 33) (dual of [2060, 1882, 34]-code), using
- discarding factors / shortening the dual code based on linear OA(2177, 2059, F2, 32) (dual of [2059, 1882, 33]-code), using
- OOA 2-folding [i] based on linear OA(2177, 2058, F2, 32) (dual of [2058, 1881, 33]-code), using
- discarding factors / shortening the dual code based on linear OOA(2177, 1029, F2, 2, 32) (dual of [(1029, 2), 1881, 33]-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.