Information on Result #1788210
Digital (108, 126, 390687)-net over F5, using embedding of OOA with Gilbert–Varšamov bound based on linear OA(5126, 390687, F5, 18) (dual of [390687, 390561, 19]-code), using
- construction X with Varšamov bound [i] based on
- linear OA(5125, 390685, F5, 18) (dual of [390685, 390560, 19]-code), using
- construction X applied to Ce(17) ⊂ Ce(10) [i] based on
- linear OA(5113, 390625, F5, 18) (dual of [390625, 390512, 19]-code), using an extension Ce(17) of the primitive narrow-sense BCH-code C(I) with length 390624 = 58−1, defining interval I = [1,17], and designed minimum distance d ≥ |I|+1 = 18 [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(512, 60, F5, 6) (dual of [60, 48, 7]-code), using
- discarding factors / shortening the dual code based on linear OA(512, 62, F5, 6) (dual of [62, 50, 7]-code), using
- the cyclic code C(A) with length 62 | 53−1, defining set A = {4,8,11,17}, and minimum distance d ≥ |{8,11,14,…,23}|+1 = 7 (BCH-bound) [i]
- discarding factors / shortening the dual code based on linear OA(512, 62, F5, 6) (dual of [62, 50, 7]-code), using
- construction X applied to Ce(17) ⊂ Ce(10) [i] based on
- linear OA(5125, 390686, F5, 17) (dual of [390686, 390561, 18]-code), using Gilbert–Varšamov bound and bm = 5125 > Vbs−1(k−1) = 60 455958 735334 502993 880184 891632 011854 498948 569514 196087 722235 075298 406401 318037 030485 [i]
- linear OA(50, 1, F5, 0) (dual of [1, 1, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(50, s, F5, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
- linear OA(5125, 390685, F5, 18) (dual of [390685, 390560, 19]-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.