Information on Result #1745920
Digital (37, 56, 78243)-net over F81, using net defined by OOA based on linear OOA(8156, 78243, F81, 21, 19) (dual of [(78243, 21), 1643047, 20]-NRT-code), using
- OOA 3-folding and stacking with additional row [i] based on linear OOA(8156, 234730, F81, 3, 19) (dual of [(234730, 3), 704134, 20]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(8156, 234732, F81, 3, 19) (dual of [(234732, 3), 704140, 20]-NRT-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(8156, 234732, F81, 2, 19) (dual of [(234732, 2), 469408, 20]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(8156, 265724, F81, 2, 19) (dual of [(265724, 2), 531392, 20]-NRT-code), using
- OOA 2-folding [i] based on linear OA(8156, 531448, F81, 19) (dual of [531448, 531392, 20]-code), using
- discarding factors / shortening the dual code based on linear OA(8156, 531449, F81, 19) (dual of [531449, 531393, 20]-code), using
- construction X applied to C([0,9]) ⊂ C([0,8]) [i] based on
- linear OA(8155, 531442, F81, 19) (dual of [531442, 531387, 20]-code), using the expurgated narrow-sense BCH-code C(I) with length 531442 | 816−1, defining interval I = [0,9], and minimum distance d ≥ |{−9,−8,…,9}|+1 = 20 (BCH-bound) [i]
- linear OA(8149, 531442, F81, 17) (dual of [531442, 531393, 18]-code), using the expurgated narrow-sense BCH-code C(I) with length 531442 | 816−1, defining interval I = [0,8], and minimum distance d ≥ |{−8,−7,…,8}|+1 = 18 (BCH-bound) [i]
- linear OA(811, 7, F81, 1) (dual of [7, 6, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(811, s, F81, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
- construction X applied to C([0,9]) ⊂ C([0,8]) [i] based on
- discarding factors / shortening the dual code based on linear OA(8156, 531449, F81, 19) (dual of [531449, 531393, 20]-code), using
- OOA 2-folding [i] based on linear OA(8156, 531448, F81, 19) (dual of [531448, 531392, 20]-code), using
- discarding factors / shortening the dual code based on linear OOA(8156, 265724, F81, 2, 19) (dual of [(265724, 2), 531392, 20]-NRT-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(8156, 234732, F81, 2, 19) (dual of [(234732, 2), 469408, 20]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(8156, 234732, F81, 3, 19) (dual of [(234732, 3), 704140, 20]-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.