Information on Result #1729420
Digital (128, 156, 52438)-net over F8, using net defined by OOA based on linear OOA(8156, 52438, F8, 33, 28) (dual of [(52438, 33), 1730298, 29]-NRT-code), using
- OOA 5-folding and stacking with additional row [i] based on linear OOA(8156, 262191, F8, 3, 28) (dual of [(262191, 3), 786417, 29]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(8156, 262192, F8, 3, 28) (dual of [(262192, 3), 786420, 29]-NRT-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(8156, 262192, F8, 28) (dual of [262192, 262036, 29]-code), using
- construction X with Varšamov bound [i] based on
- linear OA(8155, 262190, F8, 28) (dual of [262190, 262035, 29]-code), using
- construction X applied to Ce(27) ⊂ Ce(20) [i] based on
- linear OA(8145, 262144, F8, 28) (dual of [262144, 261999, 29]-code), using an extension Ce(27) of the primitive narrow-sense BCH-code C(I) with length 262143 = 86−1, defining interval I = [1,27], and designed minimum distance d ≥ |I|+1 = 28 [i]
- linear OA(8109, 262144, F8, 21) (dual of [262144, 262035, 22]-code), using an extension Ce(20) of the primitive narrow-sense BCH-code C(I) with length 262143 = 86−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [i]
- linear OA(810, 46, F8, 6) (dual of [46, 36, 7]-code), using
- discarding factors / shortening the dual code based on linear OA(810, 74, F8, 6) (dual of [74, 64, 7]-code), using
- a “GraX†code from Grassl’s database [i]
- discarding factors / shortening the dual code based on linear OA(810, 74, F8, 6) (dual of [74, 64, 7]-code), using
- construction X applied to Ce(27) ⊂ Ce(20) [i] based on
- linear OA(8155, 262191, F8, 27) (dual of [262191, 262036, 28]-code), using Gilbert–Varšamov bound and bm = 8155 > Vbs−1(k−1) = 17799 878092 242579 724217 002574 749910 542132 386391 455835 837140 161475 006679 293155 302597 125541 069658 076875 533989 062796 283167 767726 770410 732796 [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(8155, 262190, F8, 28) (dual of [262190, 262035, 29]-code), using
- construction X with Varšamov bound [i] based on
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(8156, 262192, F8, 28) (dual of [262192, 262036, 29]-code), using
- discarding factors / shortening the dual code based on linear OOA(8156, 262192, F8, 3, 28) (dual of [(262192, 3), 786420, 29]-NRT-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.