Information on Result #1711982
Digital (181, 214, 1002)-net over F2, using net defined by OOA based on linear OOA(2214, 1002, F2, 40, 33) (dual of [(1002, 40), 39866, 34]-NRT-code), using
- OOA 2-folding and stacking with additional row [i] based on linear OOA(2214, 2005, F2, 8, 33) (dual of [(2005, 8), 15826, 34]-NRT-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(2214, 2005, F2, 4, 33) (dual of [(2005, 4), 7806, 34]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(2214, 2052, F2, 4, 33) (dual of [(2052, 4), 7994, 34]-NRT-code), using
- 22 times duplication [i] based on linear OOA(2212, 2052, F2, 4, 33) (dual of [(2052, 4), 7996, 34]-NRT-code), using
- OOA 4-folding [i] based on linear OA(2212, 8208, F2, 33) (dual of [8208, 7996, 34]-code), using
- 2 times code embedding in larger space [i] based on linear OA(2210, 8206, F2, 33) (dual of [8206, 7996, 34]-code), using
- construction X applied to Ce(32) ⊂ Ce(30) [i] based on
- linear OA(2209, 8192, F2, 33) (dual of [8192, 7983, 34]-code), using an extension Ce(32) of the primitive narrow-sense BCH-code C(I) with length 8191 = 213−1, defining interval I = [1,32], and designed minimum distance d ≥ |I|+1 = 33 [i]
- linear OA(2196, 8192, F2, 31) (dual of [8192, 7996, 32]-code), using an extension Ce(30) of the primitive narrow-sense BCH-code C(I) with length 8191 = 213−1, defining interval I = [1,30], and designed minimum distance d ≥ |I|+1 = 31 [i]
- linear OA(21, 14, F2, 1) (dual of [14, 13, 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
- 2 times code embedding in larger space [i] based on linear OA(2210, 8206, F2, 33) (dual of [8206, 7996, 34]-code), using
- OOA 4-folding [i] based on linear OA(2212, 8208, F2, 33) (dual of [8208, 7996, 34]-code), using
- 22 times duplication [i] based on linear OOA(2212, 2052, F2, 4, 33) (dual of [(2052, 4), 7996, 34]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(2214, 2052, F2, 4, 33) (dual of [(2052, 4), 7994, 34]-NRT-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(2214, 2005, F2, 4, 33) (dual of [(2005, 4), 7806, 34]-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.