Information on Result #1787800
Digital (100, 117, 390679)-net over F5, using embedding of OOA with Gilbert–Varšamov bound based on linear OA(5117, 390679, F5, 17) (dual of [390679, 390562, 18]-code), using
- construction X with Varšamov bound [i] based on
- linear OA(5114, 390674, F5, 17) (dual of [390674, 390560, 18]-code), using
- construction X applied to Ce(16) ⊂ Ce(10) [i] based on
- linear OA(5105, 390625, F5, 17) (dual of [390625, 390520, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 390624 = 58−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
- linear OA(565, 390625, F5, 11) (dual of [390625, 390560, 12]-code), using an extension Ce(10) of the primitive narrow-sense BCH-code C(I) with length 390624 = 58−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [i]
- linear OA(59, 49, F5, 5) (dual of [49, 40, 6]-code), using
- discarding factors / shortening the dual code based on linear OA(59, 62, F5, 5) (dual of [62, 53, 6]-code), using
- a “GraCyc†code from Grassl’s database [i]
- discarding factors / shortening the dual code based on linear OA(59, 62, F5, 5) (dual of [62, 53, 6]-code), using
- construction X applied to Ce(16) ⊂ Ce(10) [i] based on
- linear OA(5114, 390676, F5, 15) (dual of [390676, 390562, 16]-code), using Gilbert–Varšamov bound and bm = 5114 > Vbs−1(k−1) = 5939 541861 136056 452280 740294 586875 940195 762091 848138 921475 198409 234928 441661 [i]
- linear OA(51, 3, F5, 1) (dual of [3, 2, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(51, s, F5, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
- linear OA(5114, 390674, F5, 17) (dual of [390674, 390560, 18]-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.