Information on Result #1784531
Digital (217, 252, 166521)-net over F4, using embedding of OOA with Gilbert–Varšamov bound based on linear OA(4252, 166521, F4, 35) (dual of [166521, 166269, 36]-code), using
- discarding factors / shortening the dual code based on linear OA(4252, 262213, F4, 35) (dual of [262213, 261961, 36]-code), using
- construction X applied to C([0,17]) ⊂ C([0,13]) [i] based on
- linear OA(4235, 262145, F4, 35) (dual of [262145, 261910, 36]-code), using the expurgated narrow-sense BCH-code C(I) with length 262145 | 418−1, defining interval I = [0,17], and minimum distance d ≥ |{−17,−16,…,17}|+1 = 36 (BCH-bound) [i]
- linear OA(4181, 262145, F4, 27) (dual of [262145, 261964, 28]-code), using the expurgated narrow-sense BCH-code C(I) with length 262145 | 418−1, defining interval I = [0,13], and minimum distance d ≥ |{−13,−12,…,13}|+1 = 28 (BCH-bound) [i]
- linear OA(417, 68, F4, 7) (dual of [68, 51, 8]-code), using
- generalized (u, u+v)-construction [i] based on
- linear OA(41, 17, F4, 1) (dual of [17, 16, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(41, s, F4, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
- linear OA(43, 17, F4, 2) (dual of [17, 14, 3]-code), using
- discarding factors / shortening the dual code based on linear OA(43, 21, F4, 2) (dual of [21, 18, 3]-code), using
- Hamming code H(3,4) [i]
- discarding factors / shortening the dual code based on linear OA(43, 21, F4, 2) (dual of [21, 18, 3]-code), using
- linear OA(44, 17, F4, 3) (dual of [17, 13, 4]-code or 17-cap in PG(3,4)), using
- linear OA(49, 17, F4, 7) (dual of [17, 8, 8]-code), using
- linear OA(41, 17, F4, 1) (dual of [17, 16, 2]-code), using
- generalized (u, u+v)-construction [i] based on
- construction X applied to C([0,17]) ⊂ C([0,13]) [i] based on
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.