Information on Result #1781129
Digital (183, 215, 65623)-net over F4, using embedding of OOA with Gilbert–Varšamov bound based on linear OA(4215, 65623, F4, 32) (dual of [65623, 65408, 33]-code), using
- construction X with Varšamov bound [i] based on
- linear OA(4214, 65621, F4, 32) (dual of [65621, 65407, 33]-code), using
- construction X applied to Ce(32) ⊂ Ce(21) [i] based on
- linear OA(4193, 65536, F4, 33) (dual of [65536, 65343, 34]-code), using an extension Ce(32) of the primitive narrow-sense BCH-code C(I) with length 65535 = 48−1, defining interval I = [1,32], and designed minimum distance d ≥ |I|+1 = 33 [i]
- linear OA(4129, 65536, F4, 22) (dual of [65536, 65407, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 65535 = 48−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [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(32) ⊂ Ce(21) [i] based on
- linear OA(4214, 65622, F4, 31) (dual of [65622, 65408, 32]-code), using Gilbert–Varšamov bound and bm = 4214 > Vbs−1(k−1) = 2 502936 050615 400529 190553 521166 057942 047489 632173 226640 437710 854803 543500 502033 266486 166211 686806 997824 652970 105706 716830 186336 [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(4214, 65621, F4, 32) (dual of [65621, 65407, 33]-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.