Information on Result #1722018
Digital (49, 59, 39071)-net over F5, using net defined by OOA based on linear OOA(559, 39071, F5, 15, 10) (dual of [(39071, 15), 586006, 11]-NRT-code), using
- OOA 2-folding and stacking with additional row [i] based on linear OOA(559, 78143, F5, 3, 10) (dual of [(78143, 3), 234370, 11]-NRT-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(559, 78143, F5, 10) (dual of [78143, 78084, 11]-code), using
- construction X with Varšamov bound [i] based on
- linear OA(558, 78141, F5, 10) (dual of [78141, 78083, 11]-code), using
- construction X4 applied to Ce(10) ⊂ Ce(7) [i] based on
- linear OA(557, 78125, F5, 11) (dual of [78125, 78068, 12]-code), using an extension Ce(10) of the primitive narrow-sense BCH-code C(I) with length 78124 = 57−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [i]
- linear OA(543, 78125, F5, 8) (dual of [78125, 78082, 9]-code), using an extension Ce(7) of the primitive narrow-sense BCH-code C(I) with length 78124 = 57−1, defining interval I = [1,7], and designed minimum distance d ≥ |I|+1 = 8 [i]
- linear OA(515, 16, F5, 15) (dual of [16, 1, 16]-code or 16-arc in PG(14,5)), using
- dual of repetition code with length 16 [i]
- linear OA(51, 16, F5, 1) (dual of [16, 15, 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
- construction X4 applied to Ce(10) ⊂ Ce(7) [i] based on
- linear OA(558, 78142, F5, 9) (dual of [78142, 78084, 10]-code), using Gilbert–Varšamov bound and bm = 558 > Vbs−1(k−1) = 2258 637933 317132 278470 620900 305806 471125 [i]
- linear OA(50, 1, F5, 0) (dual of [1, 1, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(50, s, F5, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
- linear OA(558, 78141, F5, 10) (dual of [78141, 78083, 11]-code), using
- construction X with Varšamov bound [i] based on
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(559, 78143, F5, 10) (dual of [78143, 78084, 11]-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.