Information on Result #1804732
Digital (42, 80, 679)-net over F25, using embedding of OOA with Gilbert–Varšamov bound based on linear OA(2580, 679, F25, 38) (dual of [679, 599, 39]-code), using
- discarding factors / shortening the dual code based on linear OA(2580, 682, F25, 38) (dual of [682, 602, 39]-code), using
- 46 step Varšamov–Edel lengthening with (ri) = (4, 1, 0, 1, 4 times 0, 1, 11 times 0, 1, 25 times 0) [i] based on linear OA(2572, 628, F25, 38) (dual of [628, 556, 39]-code), using
- construction XX applied to C1 = C([623,35]), C2 = C([0,36]), C3 = C1 + C2 = C([0,35]), and C∩ = C1 ∩ C2 = C([623,36]) [i] based on
- linear OA(2570, 624, F25, 37) (dual of [624, 554, 38]-code), using the primitive BCH-code C(I) with length 624 = 252−1, defining interval I = {−1,0,…,35}, and designed minimum distance d ≥ |I|+1 = 38 [i]
- linear OA(2570, 624, F25, 37) (dual of [624, 554, 38]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 624 = 252−1, defining interval I = [0,36], and designed minimum distance d ≥ |I|+1 = 38 [i]
- linear OA(2572, 624, F25, 38) (dual of [624, 552, 39]-code), using the primitive BCH-code C(I) with length 624 = 252−1, defining interval I = {−1,0,…,36}, and designed minimum distance d ≥ |I|+1 = 39 [i]
- linear OA(2568, 624, F25, 36) (dual of [624, 556, 37]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 624 = 252−1, defining interval I = [0,35], and designed minimum distance d ≥ |I|+1 = 37 [i]
- linear OA(250, 2, F25, 0) (dual of [2, 2, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(250, s, F25, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
- linear OA(250, 2, F25, 0) (dual of [2, 2, 1]-code) (see above)
- construction XX applied to C1 = C([623,35]), C2 = C([0,36]), C3 = C1 + C2 = C([0,35]), and C∩ = C1 ∩ C2 = C([623,36]) [i] based on
- 46 step Varšamov–Edel lengthening with (ri) = (4, 1, 0, 1, 4 times 0, 1, 11 times 0, 1, 25 times 0) [i] based on linear OA(2572, 628, F25, 38) (dual of [628, 556, 39]-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.