Information on Result #1773008
Digital (44, 63, 333)-net over F4, using embedding of OOA with Gilbert–Varšamov bound based on linear OA(463, 333, F4, 19) (dual of [333, 270, 20]-code), using
- 64 step Varšamov–Edel lengthening with (ri) = (2, 1, 0, 1, 0, 0, 0, 1, 6 times 0, 1, 11 times 0, 1, 16 times 0, 1, 20 times 0) [i] based on linear OA(455, 261, F4, 19) (dual of [261, 206, 20]-code), using
- construction XX applied to C1 = C([254,16]), C2 = C([0,17]), C3 = C1 + C2 = C([0,16]), and C∩ = C1 ∩ C2 = C([254,17]) [i] based on
- linear OA(453, 255, F4, 18) (dual of [255, 202, 19]-code), using the primitive BCH-code C(I) with length 255 = 44−1, defining interval I = {−1,0,…,16}, and designed minimum distance d ≥ |I|+1 = 19 [i]
- linear OA(451, 255, F4, 18) (dual of [255, 204, 19]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 255 = 44−1, defining interval I = [0,17], and designed minimum distance d ≥ |I|+1 = 19 [i]
- linear OA(455, 255, F4, 19) (dual of [255, 200, 20]-code), using the primitive BCH-code C(I) with length 255 = 44−1, defining interval I = {−1,0,…,17}, and designed minimum distance d ≥ |I|+1 = 20 [i]
- linear OA(449, 255, F4, 17) (dual of [255, 206, 18]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 255 = 44−1, defining interval I = [0,16], and designed minimum distance d ≥ |I|+1 = 18 [i]
- linear OA(40, 4, F4, 0) (dual of [4, 4, 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(40, 2, F4, 0) (dual of [2, 2, 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 (see above)
- construction XX applied to C1 = C([254,16]), C2 = C([0,17]), C3 = C1 + C2 = C([0,16]), and C∩ = C1 ∩ C2 = C([254,17]) [i] based on
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.