Information on Result #1813635
Digital (31, 47, 878594)-net over F128, using embedding of OOA with Gilbert–Varšamov bound based on linear OOA(12847, 878594, F128, 2, 16) (dual of [(878594, 2), 1757141, 17]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(12847, 1048579, F128, 2, 16) (dual of [(1048579, 2), 2097111, 17]-NRT-code), using
- OOA 2-folding [i] based on linear OA(12847, 2097158, F128, 16) (dual of [2097158, 2097111, 17]-code), using
- discarding factors / shortening the dual code based on linear OA(12847, 2097159, F128, 16) (dual of [2097159, 2097112, 17]-code), using
- construction X applied to Ce(15) ⊂ Ce(13) [i] based on
- linear OA(12846, 2097152, F128, 16) (dual of [2097152, 2097106, 17]-code), using an extension Ce(15) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 1283−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16 [i]
- linear OA(12840, 2097152, F128, 14) (dual of [2097152, 2097112, 15]-code), using an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 1283−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [i]
- linear OA(1281, 7, F128, 1) (dual of [7, 6, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(1281, s, F128, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
- construction X applied to Ce(15) ⊂ Ce(13) [i] based on
- discarding factors / shortening the dual code based on linear OA(12847, 2097159, F128, 16) (dual of [2097159, 2097112, 17]-code), using
- OOA 2-folding [i] based on linear OA(12847, 2097158, F128, 16) (dual of [2097158, 2097111, 17]-code), using
Mode: Linear.
Optimality
Show details for fixed k and m, k and s, k and t, m and s, m and t, t and s.
Other Results with Identical Parameters
None.
Depending Results
None.