Information on Result #1751029
Digital (103, 126, 678)-net over F2, using embedding of OOA with Gilbert–Varšamov bound based on linear OOA(2126, 678, F2, 3, 23) (dual of [(678, 3), 1908, 24]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(2126, 687, F2, 3, 23) (dual of [(687, 3), 1935, 24]-NRT-code), using
- 22 times duplication [i] based on linear OOA(2124, 687, F2, 3, 23) (dual of [(687, 3), 1937, 24]-NRT-code), using
- OOA 3-folding [i] based on linear OA(2124, 2061, F2, 23) (dual of [2061, 1937, 24]-code), using
- 1 times code embedding in larger space [i] based on linear OA(2123, 2060, F2, 23) (dual of [2060, 1937, 24]-code), using
- construction X applied to Ce(22) ⊂ Ce(20) [i] based on
- linear OA(2122, 2048, F2, 23) (dual of [2048, 1926, 24]-code), using an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 2047 = 211−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [i]
- linear OA(2111, 2048, F2, 21) (dual of [2048, 1937, 22]-code), using an extension Ce(20) of the primitive narrow-sense BCH-code C(I) with length 2047 = 211−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [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(22) ⊂ Ce(20) [i] based on
- 1 times code embedding in larger space [i] based on linear OA(2123, 2060, F2, 23) (dual of [2060, 1937, 24]-code), using
- OOA 3-folding [i] based on linear OA(2124, 2061, F2, 23) (dual of [2061, 1937, 24]-code), using
- 22 times duplication [i] based on linear OOA(2124, 687, F2, 3, 23) (dual of [(687, 3), 1937, 24]-NRT-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.