Information on Result #1718434
Digital (82, 101, 2770)-net over F4, using net defined by OOA based on linear OOA(4101, 2770, F4, 21, 19) (dual of [(2770, 21), 58069, 20]-NRT-code), using
- OOA 3-folding and stacking with additional row [i] based on linear OOA(4101, 8311, F4, 3, 19) (dual of [(8311, 3), 24832, 20]-NRT-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(4101, 8311, F4, 19) (dual of [8311, 8210, 20]-code), using
- discarding factors / shortening the dual code based on linear OA(4101, 16401, F4, 19) (dual of [16401, 16300, 20]-code), using
- 1 times code embedding in larger space [i] based on linear OA(4100, 16400, F4, 19) (dual of [16400, 16300, 20]-code), using
- construction X applied to C([0,9]) ⊂ C([0,8]) [i] based on
- linear OA(499, 16385, F4, 19) (dual of [16385, 16286, 20]-code), using the expurgated narrow-sense BCH-code C(I) with length 16385 | 414−1, defining interval I = [0,9], and minimum distance d ≥ |{−9,−8,…,9}|+1 = 20 (BCH-bound) [i]
- linear OA(485, 16385, F4, 17) (dual of [16385, 16300, 18]-code), using the expurgated narrow-sense BCH-code C(I) with length 16385 | 414−1, defining interval I = [0,8], and minimum distance d ≥ |{−8,−7,…,8}|+1 = 18 (BCH-bound) [i]
- linear OA(41, 15, F4, 1) (dual of [15, 14, 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
- construction X applied to C([0,9]) ⊂ C([0,8]) [i] based on
- 1 times code embedding in larger space [i] based on linear OA(4100, 16400, F4, 19) (dual of [16400, 16300, 20]-code), using
- discarding factors / shortening the dual code based on linear OA(4101, 16401, F4, 19) (dual of [16401, 16300, 20]-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(4101, 8311, F4, 19) (dual of [8311, 8210, 20]-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.