Information on Result #1749543
Digital (58, 78, 134)-net over F2, using embedding of OOA with Gilbert–Varšamov bound based on linear OOA(278, 134, F2, 2, 20) (dual of [(134, 2), 190, 21]-NRT-code), using
- OOA 2-folding [i] based on linear OA(278, 268, F2, 20) (dual of [268, 190, 21]-code), using
- 1 times truncation [i] based on linear OA(279, 269, F2, 21) (dual of [269, 190, 22]-code), using
- construction XX applied to C1 = C([253,16]), C2 = C([0,18]), C3 = C1 + C2 = C([0,16]), and C∩ = C1 ∩ C2 = C([253,18]) [i] based on
- linear OA(273, 255, F2, 19) (dual of [255, 182, 20]-code), using the primitive BCH-code C(I) with length 255 = 28−1, defining interval I = {−2,−1,…,16}, and designed minimum distance d ≥ |I|+1 = 20 [i]
- linear OA(269, 255, F2, 19) (dual of [255, 186, 20]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 255 = 28−1, defining interval I = [0,18], and designed minimum distance d ≥ |I|+1 = 20 [i]
- linear OA(277, 255, F2, 21) (dual of [255, 178, 22]-code), using the primitive BCH-code C(I) with length 255 = 28−1, defining interval I = {−2,−1,…,18}, and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(265, 255, F2, 17) (dual of [255, 190, 18]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 255 = 28−1, defining interval I = [0,16], and designed minimum distance d ≥ |I|+1 = 18 [i]
- linear OA(21, 9, F2, 1) (dual of [9, 8, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(21, s, F2, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
- linear OA(21, 5, F2, 1) (dual of [5, 4, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(21, s, F2, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s (see above)
- construction XX applied to C1 = C([253,16]), C2 = C([0,18]), C3 = C1 + C2 = C([0,16]), and C∩ = C1 ∩ C2 = C([253,18]) [i] based on
- 1 times truncation [i] based on linear OA(279, 269, F2, 21) (dual of [269, 190, 22]-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.