Information on Result #1792874
Digital (74, 89, 524306)-net over F8, using embedding of OOA with Gilbert–Varšamov bound based on linear OA(889, 524306, F8, 15) (dual of [524306, 524217, 16]-code), using
- construction X with Varšamov bound [i] based on
- linear OA(888, 524304, F8, 15) (dual of [524304, 524216, 16]-code), using
- trace code [i] based on linear OA(6444, 262152, F64, 15) (dual of [262152, 262108, 16]-code), using
- construction X applied to C([0,7]) ⊂ C([0,6]) [i] based on
- linear OA(6443, 262145, F64, 15) (dual of [262145, 262102, 16]-code), using the expurgated narrow-sense BCH-code C(I) with length 262145 | 646−1, defining interval I = [0,7], and minimum distance d ≥ |{−7,−6,…,7}|+1 = 16 (BCH-bound) [i]
- linear OA(6437, 262145, F64, 13) (dual of [262145, 262108, 14]-code), using the expurgated narrow-sense BCH-code C(I) with length 262145 | 646−1, defining interval I = [0,6], and minimum distance d ≥ |{−6,−5,…,6}|+1 = 14 (BCH-bound) [i]
- linear OA(641, 7, F64, 1) (dual of [7, 6, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(641, s, F64, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
- construction X applied to C([0,7]) ⊂ C([0,6]) [i] based on
- trace code [i] based on linear OA(6444, 262152, F64, 15) (dual of [262152, 262108, 16]-code), using
- linear OA(888, 524305, F8, 14) (dual of [524305, 524217, 15]-code), using Gilbert–Varšamov bound and bm = 888 > Vbs−1(k−1) = 3519 754360 311078 247598 767231 296367 212708 937478 219662 564852 787360 440423 975191 [i]
- linear OA(80, 1, F8, 0) (dual of [1, 1, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(80, s, F8, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
- linear OA(888, 524304, F8, 15) (dual of [524304, 524216, 16]-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.