Information on Result #1788806
Digital (115, 138, 78172)-net over F5, using embedding of OOA with Gilbert–Varšamov bound based on linear OA(5138, 78172, F5, 23) (dual of [78172, 78034, 24]-code), using
- construction X with Varšamov bound [i] based on
- linear OA(5136, 78169, F5, 23) (dual of [78169, 78033, 24]-code), using
- construction X applied to Ce(22) ⊂ Ce(16) [i] based on
- linear OA(5127, 78125, F5, 23) (dual of [78125, 77998, 24]-code), using an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 78124 = 57−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [i]
- linear OA(592, 78125, F5, 17) (dual of [78125, 78033, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 78124 = 57−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
- linear OA(59, 44, F5, 5) (dual of [44, 35, 6]-code), using
- construction X applied to Ce(22) ⊂ Ce(16) [i] based on
- linear OA(5136, 78170, F5, 21) (dual of [78170, 78034, 22]-code), using Gilbert–Varšamov bound and bm = 5136 > Vbs−1(k−1) = 32 714359 513332 999726 313542 034775 151021 407241 742771 897852 108779 094423 408600 157540 183212 247845 [i]
- linear OA(51, 2, F5, 1) (dual of [2, 1, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(51, s, F5, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
- linear OA(5136, 78169, F5, 23) (dual of [78169, 78033, 24]-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.