Information on Result #1657535
Linear OOA(2175, 389, F2, 6, 31) (dual of [(389, 6), 2159, 32]-NRT-code), using OOA 2-folding based on linear OOA(2175, 778, F2, 3, 31) (dual of [(778, 3), 2159, 32]-NRT-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(2175, 778, F2, 2, 31) (dual of [(778, 2), 1381, 32]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(2175, 1039, F2, 2, 31) (dual of [(1039, 2), 1903, 32]-NRT-code), using
- 21 times duplication [i] based on linear OOA(2174, 1039, F2, 2, 31) (dual of [(1039, 2), 1904, 32]-NRT-code), using
- 1 times NRT-code embedding in larger space [i] based on linear OOA(2172, 1038, F2, 2, 31) (dual of [(1038, 2), 1904, 32]-NRT-code), using
- OOA 2-folding [i] based on linear OA(2172, 2076, F2, 31) (dual of [2076, 1904, 32]-code), using
- construction X applied to Ce(30) ⊂ Ce(26) [i] based on
- 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(2144, 2048, F2, 27) (dual of [2048, 1904, 28]-code), using an extension Ce(26) of the primitive narrow-sense BCH-code C(I) with length 2047 = 211−1, defining interval I = [1,26], and designed minimum distance d ≥ |I|+1 = 27 [i]
- linear OA(26, 28, F2, 3) (dual of [28, 22, 4]-code or 28-cap in PG(5,2)), using
- discarding factors / shortening the dual code based on linear OA(26, 32, F2, 3) (dual of [32, 26, 4]-code or 32-cap in PG(5,2)), using
- construction X applied to Ce(30) ⊂ Ce(26) [i] based on
- OOA 2-folding [i] based on linear OA(2172, 2076, F2, 31) (dual of [2076, 1904, 32]-code), using
- 1 times NRT-code embedding in larger space [i] based on linear OOA(2172, 1038, F2, 2, 31) (dual of [(1038, 2), 1904, 32]-NRT-code), using
- 21 times duplication [i] based on linear OOA(2174, 1039, F2, 2, 31) (dual of [(1039, 2), 1904, 32]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(2175, 1039, F2, 2, 31) (dual of [(1039, 2), 1903, 32]-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.