Information on Result #1785813
Digital (45, 56, 15657)-net over F5, using embedding of OOA with Gilbert–Varšamov bound based on linear OA(556, 15657, F5, 11) (dual of [15657, 15601, 12]-code), using
- construction X with Varšamov bound [i] based on
- linear OA(555, 15655, F5, 11) (dual of [15655, 15600, 12]-code), using
- construction X applied to Ce(10) ⊂ Ce(5) [i] based on
- linear OA(549, 15625, F5, 11) (dual of [15625, 15576, 12]-code), using an extension Ce(10) of the primitive narrow-sense BCH-code C(I) with length 15624 = 56−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [i]
- linear OA(525, 15625, F5, 6) (dual of [15625, 15600, 7]-code), using an extension Ce(5) of the primitive narrow-sense BCH-code C(I) with length 15624 = 56−1, defining interval I = [1,5], and designed minimum distance d ≥ |I|+1 = 6 [i]
- linear OA(56, 30, F5, 4) (dual of [30, 24, 5]-code), using
- construction X applied to Ce(10) ⊂ Ce(5) [i] based on
- linear OA(555, 15656, F5, 10) (dual of [15656, 15601, 11]-code), using Gilbert–Varšamov bound and bm = 555 > Vbs−1(k−1) = 40 711594 561041 026427 089149 653605 443245 [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(555, 15655, F5, 11) (dual of [15655, 15600, 12]-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.