Information on Result #1773098
Digital (50, 67, 943)-net over F4, using embedding of OOA with Gilbert–Varšamov bound based on linear OA(467, 943, F4, 17) (dual of [943, 876, 18]-code), using
- discarding factors / shortening the dual code based on linear OA(467, 1049, F4, 17) (dual of [1049, 982, 18]-code), using
- construction XX applied to C1 = C([1019,10]), C2 = C([0,12]), C3 = C1 + C2 = C([0,10]), and C∩ = C1 ∩ C2 = C([1019,12]) [i] based on
- linear OA(456, 1023, F4, 15) (dual of [1023, 967, 16]-code), using the primitive BCH-code C(I) with length 1023 = 45−1, defining interval I = {−4,−3,…,10}, and designed minimum distance d ≥ |I|+1 = 16 [i]
- linear OA(446, 1023, F4, 13) (dual of [1023, 977, 14]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 1023 = 45−1, defining interval I = [0,12], and designed minimum distance d ≥ |I|+1 = 14 [i]
- linear OA(461, 1023, F4, 17) (dual of [1023, 962, 18]-code), using the primitive BCH-code C(I) with length 1023 = 45−1, defining interval I = {−4,−3,…,12}, and designed minimum distance d ≥ |I|+1 = 18 [i]
- linear OA(441, 1023, F4, 11) (dual of [1023, 982, 12]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 1023 = 45−1, defining interval I = [0,10], and designed minimum distance d ≥ |I|+1 = 12 [i]
- linear OA(45, 20, F4, 3) (dual of [20, 15, 4]-code or 20-cap in PG(4,4)), using
- discarding factors / shortening the dual code based on linear OA(45, 41, F4, 3) (dual of [41, 36, 4]-code or 41-cap in PG(4,4)), using
- linear OA(41, 6, F4, 1) (dual of [6, 5, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(41, s, F4, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
- construction XX applied to C1 = C([1019,10]), C2 = C([0,12]), C3 = C1 + C2 = C([0,10]), and C∩ = C1 ∩ C2 = C([1019,12]) [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.