Information on Result #1210835
Digital (234, 253, 3728522)-net over F4, using (u, u+v)-construction based on
- digital (24, 33, 258)-net over F4, using
- net defined by OOA [i] based on linear OOA(433, 258, F4, 9, 9) (dual of [(258, 9), 2289, 10]-NRT-code), using
- OOA 4-folding and stacking with additional row [i] based on linear OA(433, 1033, F4, 9) (dual of [1033, 1000, 10]-code), using
- discarding factors / shortening the dual code based on linear OA(433, 1035, F4, 9) (dual of [1035, 1002, 10]-code), using
- construction XX applied to C1 = C([339,345]), C2 = C([337,343]), C3 = C1 + C2 = C([339,343]), and C∩ = C1 ∩ C2 = C([337,345]) [i] based on
- linear OA(426, 1023, F4, 7) (dual of [1023, 997, 8]-code), using the primitive BCH-code C(I) with length 1023 = 45−1, defining interval I = {339,340,…,345}, and designed minimum distance d ≥ |I|+1 = 8 [i]
- linear OA(426, 1023, F4, 7) (dual of [1023, 997, 8]-code), using the primitive BCH-code C(I) with length 1023 = 45−1, defining interval I = {337,338,…,343}, and designed minimum distance d ≥ |I|+1 = 8 [i]
- linear OA(431, 1023, F4, 9) (dual of [1023, 992, 10]-code), using the primitive BCH-code C(I) with length 1023 = 45−1, defining interval I = {337,338,…,345}, and designed minimum distance d ≥ |I|+1 = 10 [i]
- linear OA(421, 1023, F4, 5) (dual of [1023, 1002, 6]-code), using the primitive BCH-code C(I) with length 1023 = 45−1, defining interval I = {339,340,341,342,343}, and designed minimum distance d ≥ |I|+1 = 6 [i]
- 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
- linear OA(41, 6, F4, 1) (dual of [6, 5, 2]-code) (see above)
- construction XX applied to C1 = C([339,345]), C2 = C([337,343]), C3 = C1 + C2 = C([339,343]), and C∩ = C1 ∩ C2 = C([337,345]) [i] based on
- discarding factors / shortening the dual code based on linear OA(433, 1035, F4, 9) (dual of [1035, 1002, 10]-code), using
- OOA 4-folding and stacking with additional row [i] based on linear OA(433, 1033, F4, 9) (dual of [1033, 1000, 10]-code), using
- net defined by OOA [i] based on linear OOA(433, 258, F4, 9, 9) (dual of [(258, 9), 2289, 10]-NRT-code), using
- digital (201, 220, 3728264)-net over F4, using
- trace code for nets [i] based on digital (36, 55, 932066)-net over F256, using
- net defined by OOA [i] based on linear OOA(25655, 932066, F256, 19, 19) (dual of [(932066, 19), 17709199, 20]-NRT-code), using
- OOA 9-folding and stacking with additional row [i] based on linear OA(25655, 8388595, F256, 19) (dual of [8388595, 8388540, 20]-code), using
- discarding factors / shortening the dual code based on linear OA(25655, large, F256, 19) (dual of [large, large−55, 20]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 16777215 = 2563−1, defining interval I = [0,18], and designed minimum distance d ≥ |I|+1 = 20 [i]
- discarding factors / shortening the dual code based on linear OA(25655, large, F256, 19) (dual of [large, large−55, 20]-code), using
- OOA 9-folding and stacking with additional row [i] based on linear OA(25655, 8388595, F256, 19) (dual of [8388595, 8388540, 20]-code), using
- net defined by OOA [i] based on linear OOA(25655, 932066, F256, 19, 19) (dual of [(932066, 19), 17709199, 20]-NRT-code), using
- trace code for nets [i] based on digital (36, 55, 932066)-net over F256, using
Mode: Constructive and 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.