Information on Result #1746328
Digital (27, 52, 816)-net over F81, using net defined by OOA based on linear OOA(8152, 816, F81, 28, 25) (dual of [(816, 28), 22796, 26]-NRT-code), using
- OOA 3-folding and stacking with additional row [i] based on linear OOA(8152, 2449, F81, 4, 25) (dual of [(2449, 4), 9744, 26]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(8152, 2451, F81, 4, 25) (dual of [(2451, 4), 9752, 26]-NRT-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(8152, 2451, F81, 2, 25) (dual of [(2451, 2), 4850, 26]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(8152, 3286, F81, 2, 25) (dual of [(3286, 2), 6520, 26]-NRT-code), using
- OOA 2-folding [i] based on linear OA(8152, 6572, F81, 25) (dual of [6572, 6520, 26]-code), using
- discarding factors / shortening the dual code based on linear OA(8152, 6573, F81, 25) (dual of [6573, 6521, 26]-code), using
- construction X applied to C([0,12]) ⊂ C([0,10]) [i] based on
- 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(8141, 6562, F81, 21) (dual of [6562, 6521, 22]-code), using the expurgated narrow-sense BCH-code C(I) with length 6562 | 814−1, defining interval I = [0,10], and minimum distance d ≥ |{−10,−9,…,10}|+1 = 22 (BCH-bound) [i]
- linear OA(813, 11, F81, 3) (dual of [11, 8, 4]-code or 11-arc in PG(2,81) or 11-cap in PG(2,81)), using
- discarding factors / shortening the dual code based on linear OA(813, 81, F81, 3) (dual of [81, 78, 4]-code or 81-arc in PG(2,81) or 81-cap in PG(2,81)), using
- Reed–Solomon code RS(78,81) [i]
- discarding factors / shortening the dual code based on linear OA(813, 81, F81, 3) (dual of [81, 78, 4]-code or 81-arc in PG(2,81) or 81-cap in PG(2,81)), using
- construction X applied to C([0,12]) ⊂ C([0,10]) [i] based on
- discarding factors / shortening the dual code based on linear OA(8152, 6573, F81, 25) (dual of [6573, 6521, 26]-code), using
- OOA 2-folding [i] based on linear OA(8152, 6572, F81, 25) (dual of [6572, 6520, 26]-code), using
- discarding factors / shortening the dual code based on linear OOA(8152, 3286, F81, 2, 25) (dual of [(3286, 2), 6520, 26]-NRT-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(8152, 2451, F81, 2, 25) (dual of [(2451, 2), 4850, 26]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(8152, 2451, F81, 4, 25) (dual of [(2451, 4), 9752, 26]-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.