Information on Result #1703519
Linear OOA(2217, 2217, F2, 8, 32) (dual of [(2217, 8), 17519, 33]-NRT-code), using embedding of OOA with Gilbert–Varšamov bound based on linear OOA(2217, 2217, F2, 3, 32) (dual of [(2217, 3), 6434, 33]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(2217, 2742, F2, 3, 32) (dual of [(2742, 3), 8009, 33]-NRT-code), using
- 21 times duplication [i] based on linear OOA(2216, 2742, F2, 3, 32) (dual of [(2742, 3), 8010, 33]-NRT-code), using
- OOA 3-folding [i] based on linear OA(2216, 8226, F2, 32) (dual of [8226, 8010, 33]-code), using
- 2 times code embedding in larger space [i] based on linear OA(2214, 8224, F2, 32) (dual of [8224, 8010, 33]-code), using
- 1 times truncation [i] 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
- 1 times truncation [i] based on linear OA(2215, 8225, F2, 33) (dual of [8225, 8010, 34]-code), using
- 2 times code embedding in larger space [i] based on linear OA(2214, 8224, F2, 32) (dual of [8224, 8010, 33]-code), using
- OOA 3-folding [i] based on linear OA(2216, 8226, F2, 32) (dual of [8226, 8010, 33]-code), using
- 21 times duplication [i] based on linear OOA(2216, 2742, F2, 3, 32) (dual of [(2742, 3), 8010, 33]-NRT-code), using
Mode: Linear.
Optimality
Show details for fixed k and m, n and k, k and s, k and t, n and m, m and s, m and t, n and s, n and t.
Other Results with Identical Parameters
None.
Depending Results
The following results depend on this result:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | Linear OOA(2217, 1108, F2, 40, 32) (dual of [(1108, 40), 44103, 33]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |