Information on Result #1095703
Linear OOA(2135, 13113, F2, 5, 17) (dual of [(13113, 5), 65430, 18]-NRT-code), using OOA 5-folding based on linear OA(2135, 65565, F2, 17) (dual of [65565, 65430, 18]-code), using
- discarding factors / shortening the dual code based on linear OA(2135, 65569, F2, 17) (dual of [65569, 65434, 18]-code), using
- construction X applied to C([0,8]) ⊂ C([0,6]) [i] based on
- linear OA(2129, 65537, F2, 17) (dual of [65537, 65408, 18]-code), using the expurgated narrow-sense BCH-code C(I) with length 65537 | 232−1, defining interval I = [0,8], and minimum distance d ≥ |{−8,−7,…,8}|+1 = 18 (BCH-bound) [i]
- linear OA(297, 65537, F2, 13) (dual of [65537, 65440, 14]-code), using the expurgated narrow-sense BCH-code C(I) with length 65537 | 232−1, defining interval I = [0,6], and minimum distance d ≥ |{−6,−5,…,6}|+1 = 14 (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([0,8]) ⊂ C([0,6]) [i] based on
Mode: Constructive and 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(2135, 13113, F2, 6, 17) (dual of [(13113, 6), 78543, 18]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(2135, 13113, F2, 7, 17) (dual of [(13113, 7), 91656, 18]-NRT-code) | [i] | ||
| 3 | Linear OOA(2135, 13113, F2, 8, 17) (dual of [(13113, 8), 104769, 18]-NRT-code) | [i] | ||
| 4 | Digital (118, 135, 13113)-net over F2 | [i] | ||