Information on Result #1780459
Digital (176, 207, 65623)-net over F4, using embedding of OOA with Gilbert–Varšamov bound based on linear OA(4207, 65623, F4, 31) (dual of [65623, 65416, 32]-code), using
- construction X with Varšamov bound [i] based on
- linear OA(4206, 65621, F4, 31) (dual of [65621, 65415, 32]-code), using
- construction X applied to Ce(30) ⊂ Ce(20) [i] based on
- linear OA(4185, 65536, F4, 31) (dual of [65536, 65351, 32]-code), using an extension Ce(30) of the primitive narrow-sense BCH-code C(I) with length 65535 = 48−1, defining interval I = [1,30], and designed minimum distance d ≥ |I|+1 = 31 [i]
- linear OA(4121, 65536, F4, 21) (dual of [65536, 65415, 22]-code), using an extension Ce(20) of the primitive narrow-sense BCH-code C(I) with length 65535 = 48−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [i]
- linear OA(421, 85, F4, 9) (dual of [85, 64, 10]-code), using
- discarding factors / shortening the dual code based on linear OA(421, 86, F4, 9) (dual of [86, 65, 10]-code), using
- construction X applied to Ce(30) ⊂ Ce(20) [i] based on
- linear OA(4206, 65622, F4, 30) (dual of [65622, 65416, 31]-code), using Gilbert–Varšamov bound and bm = 4206 > Vbs−1(k−1) = 381 589724 883936 498023 297673 565779 660837 181532 080839 077730 990767 589530 616414 333849 409116 494121 178902 114688 283165 970092 699392 [i]
- linear OA(40, 1, F4, 0) (dual of [1, 1, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(40, s, F4, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
- linear OA(4206, 65621, F4, 31) (dual of [65621, 65415, 32]-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.