Information on Result #1743322
Digital (29, 44, 19609)-net over F49, using net defined by OOA based on linear OOA(4944, 19609, F49, 21, 15) (dual of [(19609, 21), 411745, 16]-NRT-code), using
- OOA 3-folding and stacking with additional row [i] based on linear OOA(4944, 58828, F49, 3, 15) (dual of [(58828, 3), 176440, 16]-NRT-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(4944, 58828, F49, 2, 15) (dual of [(58828, 2), 117612, 16]-NRT-code), using
- OOA 2-folding [i] based on linear OA(4944, 117656, F49, 15) (dual of [117656, 117612, 16]-code), using
- discarding factors / shortening the dual code based on linear OA(4944, 117657, F49, 15) (dual of [117657, 117613, 16]-code), using
- construction X applied to C([0,7]) ⊂ C([0,6]) [i] based on
- linear OA(4943, 117650, F49, 15) (dual of [117650, 117607, 16]-code), using the expurgated narrow-sense BCH-code C(I) with length 117650 | 496−1, defining interval I = [0,7], and minimum distance d ≥ |{−7,−6,…,7}|+1 = 16 (BCH-bound) [i]
- linear OA(4937, 117650, F49, 13) (dual of [117650, 117613, 14]-code), using the expurgated narrow-sense BCH-code C(I) with length 117650 | 496−1, defining interval I = [0,6], and minimum distance d ≥ |{−6,−5,…,6}|+1 = 14 (BCH-bound) [i]
- linear OA(491, 7, F49, 1) (dual of [7, 6, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(491, s, F49, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
- construction X applied to C([0,7]) ⊂ C([0,6]) [i] based on
- discarding factors / shortening the dual code based on linear OA(4944, 117657, F49, 15) (dual of [117657, 117613, 16]-code), using
- OOA 2-folding [i] based on linear OA(4944, 117656, F49, 15) (dual of [117656, 117612, 16]-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(4944, 58828, F49, 2, 15) (dual of [(58828, 2), 117612, 16]-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.