Information on Result #1732916
Digital (81, 108, 2626)-net over F9, using net defined by OOA based on linear OOA(9108, 2626, F9, 33, 27) (dual of [(2626, 33), 86550, 28]-NRT-code), using
- OOA 5-folding and stacking with additional row [i] based on linear OOA(9108, 13131, F9, 3, 27) (dual of [(13131, 3), 39285, 28]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(9108, 13134, F9, 3, 27) (dual of [(13134, 3), 39294, 28]-NRT-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(9108, 13134, F9, 27) (dual of [13134, 13026, 28]-code), using
- trace code [i] based on linear OA(8154, 6567, F81, 27) (dual of [6567, 6513, 28]-code), using
- construction X applied to C([0,13]) ⊂ C([0,12]) [i] based on
- linear OA(8153, 6562, F81, 27) (dual of [6562, 6509, 28]-code), using the expurgated narrow-sense BCH-code C(I) with length 6562 | 814−1, defining interval I = [0,13], and minimum distance d ≥ |{−13,−12,…,13}|+1 = 28 (BCH-bound) [i]
- linear OA(8149, 6562, F81, 25) (dual of [6562, 6513, 26]-code), using the expurgated narrow-sense BCH-code C(I) with length 6562 | 814−1, defining interval I = [0,12], and minimum distance d ≥ |{−12,−11,…,12}|+1 = 26 (BCH-bound) [i]
- linear OA(811, 5, F81, 1) (dual of [5, 4, 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([0,13]) ⊂ C([0,12]) [i] based on
- trace code [i] based on linear OA(8154, 6567, F81, 27) (dual of [6567, 6513, 28]-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(9108, 13134, F9, 27) (dual of [13134, 13026, 28]-code), using
- discarding factors / shortening the dual code based on linear OOA(9108, 13134, F9, 3, 27) (dual of [(13134, 3), 39294, 28]-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.