Information on Result #1721368
Digital (219, 259, 8750)-net over F4, using net defined by OOA based on linear OOA(4259, 8750, F4, 45, 40) (dual of [(8750, 45), 393491, 41]-NRT-code), using
- OOA 7-folding and stacking with additional row [i] based on linear OOA(4259, 61251, F4, 3, 40) (dual of [(61251, 3), 183494, 41]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(4259, 61254, F4, 3, 40) (dual of [(61254, 3), 183503, 41]-NRT-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(4259, 61254, F4, 40) (dual of [61254, 60995, 41]-code), using
- discarding factors / shortening the dual code based on linear OA(4259, 65603, F4, 40) (dual of [65603, 65344, 41]-code), using
- 5 times code embedding in larger space [i] based on linear OA(4254, 65598, F4, 40) (dual of [65598, 65344, 41]-code), using
- construction X applied to C([0,20]) ⊂ C([0,16]) [i] based on
- linear OA(4241, 65537, F4, 41) (dual of [65537, 65296, 42]-code), using the expurgated narrow-sense BCH-code C(I) with length 65537 | 416−1, defining interval I = [0,20], and minimum distance d ≥ |{−20,−19,…,20}|+1 = 42 (BCH-bound) [i]
- linear OA(4193, 65537, F4, 33) (dual of [65537, 65344, 34]-code), using the expurgated narrow-sense BCH-code C(I) with length 65537 | 416−1, defining interval I = [0,16], and minimum distance d ≥ |{−16,−15,…,16}|+1 = 34 (BCH-bound) [i]
- linear OA(413, 61, F4, 6) (dual of [61, 48, 7]-code), using
- discarding factors / shortening the dual code based on linear OA(413, 63, F4, 6) (dual of [63, 50, 7]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 63 = 43−1, defining interval I = [0,5], and designed minimum distance d ≥ |I|+1 = 7 [i]
- discarding factors / shortening the dual code based on linear OA(413, 63, F4, 6) (dual of [63, 50, 7]-code), using
- construction X applied to C([0,20]) ⊂ C([0,16]) [i] based on
- 5 times code embedding in larger space [i] based on linear OA(4254, 65598, F4, 40) (dual of [65598, 65344, 41]-code), using
- discarding factors / shortening the dual code based on linear OA(4259, 65603, F4, 40) (dual of [65603, 65344, 41]-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(4259, 61254, F4, 40) (dual of [61254, 60995, 41]-code), using
- discarding factors / shortening the dual code based on linear OOA(4259, 61254, F4, 3, 40) (dual of [(61254, 3), 183503, 41]-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.