Information on Result #1785777
Digital (45, 54, 78151)-net over F5, using embedding of OOA with Gilbert–Varšamov bound based on linear OA(554, 78151, F5, 9) (dual of [78151, 78097, 10]-code), using
- construction X with Varšamov bound [i] based on
- linear OA(553, 78149, F5, 9) (dual of [78149, 78096, 10]-code), using
- construction X applied to Ce(8) ⊂ Ce(5) [i] based on
- linear OA(550, 78125, F5, 9) (dual of [78125, 78075, 10]-code), using an extension Ce(8) of the primitive narrow-sense BCH-code C(I) with length 78124 = 57−1, defining interval I = [1,8], and designed minimum distance d ≥ |I|+1 = 9 [i]
- linear OA(529, 78125, F5, 6) (dual of [78125, 78096, 7]-code), using an extension Ce(5) of the primitive narrow-sense BCH-code C(I) with length 78124 = 57−1, defining interval I = [1,5], and designed minimum distance d ≥ |I|+1 = 6 [i]
- linear OA(53, 24, F5, 2) (dual of [24, 21, 3]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 24 = 52−1, defining interval I = [0,1], and designed minimum distance d ≥ |I|+1 = 3 [i]
- construction X applied to Ce(8) ⊂ Ce(5) [i] based on
- linear OA(553, 78150, F5, 8) (dual of [78150, 78097, 9]-code), using Gilbert–Varšamov bound and bm = 553 > Vbs−1(k−1) = 57855 732842 240392 377082 162564 064053 [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(553, 78149, F5, 9) (dual of [78149, 78096, 10]-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.