Information on Result #1791259
Digital (84, 100, 823587)-net over F7, using embedding of OOA with Gilbert–Varšamov bound based on linear OA(7100, 823587, F7, 16) (dual of [823587, 823487, 17]-code), using
- construction X with Varšamov bound [i] based on
- linear OA(799, 823585, F7, 16) (dual of [823585, 823486, 17]-code), using
- construction X applied to Ce(15) ⊂ Ce(9) [i] based on
- linear OA(792, 823543, F7, 16) (dual of [823543, 823451, 17]-code), using an extension Ce(15) of the primitive narrow-sense BCH-code C(I) with length 823542 = 77−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16 [i]
- linear OA(757, 823543, F7, 10) (dual of [823543, 823486, 11]-code), using an extension Ce(9) of the primitive narrow-sense BCH-code C(I) with length 823542 = 77−1, defining interval I = [1,9], and designed minimum distance d ≥ |I|+1 = 10 [i]
- linear OA(77, 42, F7, 5) (dual of [42, 35, 6]-code), using
- discarding factors / shortening the dual code based on linear OA(77, 43, F7, 5) (dual of [43, 36, 6]-code), using
- construction X applied to Ce(15) ⊂ Ce(9) [i] based on
- linear OA(799, 823586, F7, 15) (dual of [823586, 823487, 16]-code), using Gilbert–Varšamov bound and bm = 799 > Vbs−1(k−1) = 59371 824060 408616 172609 415074 459024 267183 670803 108891 412435 509686 674427 305501 787399 [i]
- linear OA(70, 1, F7, 0) (dual of [1, 1, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(70, s, F7, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
- linear OA(799, 823585, F7, 16) (dual of [823585, 823486, 17]-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.