Information on Result #1773360
Digital (64, 77, 32778)-net over F4, using embedding of OOA with Gilbert–Varšamov bound based on linear OOA(477, 32778, F4, 2, 13) (dual of [(32778, 2), 65479, 14]-NRT-code), using
- OOA 2-folding [i] based on linear OA(477, 65556, F4, 13) (dual of [65556, 65479, 14]-code), using
- discarding factors / shortening the dual code based on linear OA(477, 65557, F4, 13) (dual of [65557, 65480, 14]-code), using
- construction XX applied to Ce(12) ⊂ Ce(9) ⊂ Ce(8) [i] based on
- linear OA(473, 65536, F4, 13) (dual of [65536, 65463, 14]-code), using an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 65535 = 48−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
- linear OA(457, 65536, F4, 10) (dual of [65536, 65479, 11]-code), using an extension Ce(9) of the primitive narrow-sense BCH-code C(I) with length 65535 = 48−1, defining interval I = [1,9], and designed minimum distance d ≥ |I|+1 = 10 [i]
- linear OA(449, 65536, F4, 9) (dual of [65536, 65487, 10]-code), using an extension Ce(8) of the primitive narrow-sense BCH-code C(I) with length 65535 = 48−1, defining interval I = [1,8], and designed minimum distance d ≥ |I|+1 = 9 [i]
- linear OA(43, 20, F4, 2) (dual of [20, 17, 3]-code), using
- discarding factors / shortening the dual code based on linear OA(43, 21, F4, 2) (dual of [21, 18, 3]-code), using
- Hamming code H(3,4) [i]
- discarding factors / shortening the dual code based on linear OA(43, 21, F4, 2) (dual of [21, 18, 3]-code), using
- linear OA(40, 1, F4, 0) (dual of [1, 1, 1]-code), using
- dual of repetition code with length 1 [i]
- construction XX applied to Ce(12) ⊂ Ce(9) ⊂ Ce(8) [i] based on
- discarding factors / shortening the dual code based on linear OA(477, 65557, F4, 13) (dual of [65557, 65480, 14]-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.