Information on Result #1707457
Digital (25, 29, 16399)-net over F2, using net defined by OOA based on linear OOA(229, 16399, F2, 4, 4) (dual of [(16399, 4), 65567, 5]-NRT-code), using
- appending kth column [i] based on linear OOA(229, 16399, F2, 3, 4) (dual of [(16399, 3), 49168, 5]-NRT-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(229, 16399, F2, 4) (dual of [16399, 16370, 5]-code), using
- 1 times truncation [i] based on linear OA(230, 16400, F2, 5) (dual of [16400, 16370, 6]-code), using
- construction X4 applied to Ce(4) ⊂ Ce(2) [i] based on
- linear OA(229, 16384, F2, 5) (dual of [16384, 16355, 6]-code), using an extension Ce(4) of the primitive narrow-sense BCH-code C(I) with length 16383 = 214−1, defining interval I = [1,4], and designed minimum distance d ≥ |I|+1 = 5 [i]
- linear OA(215, 16384, F2, 3) (dual of [16384, 16369, 4]-code or 16384-cap in PG(14,2)), using an extension Ce(2) of the primitive narrow-sense BCH-code C(I) with length 16383 = 214−1, defining interval I = [1,2], and designed minimum distance d ≥ |I|+1 = 3 [i]
- linear OA(215, 16, F2, 15) (dual of [16, 1, 16]-code or 16-arc in PG(14,2)), using
- dual of repetition code with length 16 [i]
- linear OA(21, 16, F2, 1) (dual of [16, 15, 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 X4 applied to Ce(4) ⊂ Ce(2) [i] based on
- 1 times truncation [i] based on linear OA(230, 16400, F2, 5) (dual of [16400, 16370, 6]-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(229, 16399, F2, 4) (dual of [16399, 16370, 5]-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.