Information on Result #1756389
Digital (183, 215, 2108)-net over F2, using embedding of OOA with Gilbert–Varšamov bound based on linear OOA(2215, 2108, F2, 3, 32) (dual of [(2108, 3), 6109, 33]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(2215, 2741, F2, 3, 32) (dual of [(2741, 3), 8008, 33]-NRT-code), using
- strength reduction [i] based on linear OOA(2215, 2741, F2, 3, 33) (dual of [(2741, 3), 8008, 34]-NRT-code), using
- OOA 3-folding [i] based on linear OA(2215, 8223, F2, 33) (dual of [8223, 8008, 34]-code), using
- discarding factors / shortening the dual code based on linear OA(2215, 8225, F2, 33) (dual of [8225, 8010, 34]-code), using
- construction X applied to C([0,16]) ⊂ C([0,14]) [i] based on
- linear OA(2209, 8193, F2, 33) (dual of [8193, 7984, 34]-code), using the expurgated narrow-sense BCH-code C(I) with length 8193 | 226−1, defining interval I = [0,16], and minimum distance d ≥ |{−16,−15,…,16}|+1 = 34 (BCH-bound) [i]
- linear OA(2183, 8193, F2, 29) (dual of [8193, 8010, 30]-code), using the expurgated narrow-sense BCH-code C(I) with length 8193 | 226−1, defining interval I = [0,14], and minimum distance d ≥ |{−14,−13,…,14}|+1 = 30 (BCH-bound) [i]
- linear OA(26, 32, F2, 3) (dual of [32, 26, 4]-code or 32-cap in PG(5,2)), using
- construction X applied to C([0,16]) ⊂ C([0,14]) [i] based on
- discarding factors / shortening the dual code based on linear OA(2215, 8225, F2, 33) (dual of [8225, 8010, 34]-code), using
- OOA 3-folding [i] based on linear OA(2215, 8223, F2, 33) (dual of [8223, 8008, 34]-code), using
- strength reduction [i] based on linear OOA(2215, 2741, F2, 3, 33) (dual of [(2741, 3), 8008, 34]-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.