Information on Result #1096485
Linear OOA(2204, 13116, F2, 5, 25) (dual of [(13116, 5), 65376, 26]-NRT-code), using OOA 5-folding based on linear OA(2204, 65580, F2, 25) (dual of [65580, 65376, 26]-code), using
- 4 times code embedding in larger space [i] based on linear OA(2200, 65576, F2, 25) (dual of [65576, 65376, 26]-code), using
- construction X applied to C([0,12]) ⊂ C([0,10]) [i] based on
- linear OA(2193, 65537, F2, 25) (dual of [65537, 65344, 26]-code), using the expurgated narrow-sense BCH-code C(I) with length 65537 | 232−1, defining interval I = [0,12], and minimum distance d ≥ |{−12,−11,…,12}|+1 = 26 (BCH-bound) [i]
- linear OA(2161, 65537, F2, 21) (dual of [65537, 65376, 22]-code), using the expurgated narrow-sense BCH-code C(I) with length 65537 | 232−1, defining interval I = [0,10], and minimum distance d ≥ |{−10,−9,…,10}|+1 = 22 (BCH-bound) [i]
- linear OA(27, 39, F2, 3) (dual of [39, 32, 4]-code or 39-cap in PG(6,2)), using
- discarding factors / shortening the dual code based on linear OA(27, 63, F2, 3) (dual of [63, 56, 4]-code or 63-cap in PG(6,2)), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 63 = 26−1, defining interval I = [0,1], and designed minimum distance d ≥ |I|+1 = 4 [i]
- discarding factors / shortening the dual code based on linear OA(27, 63, F2, 3) (dual of [63, 56, 4]-code or 63-cap in PG(6,2)), using
- construction X applied to C([0,12]) ⊂ C([0,10]) [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(2203, 13115, F2, 5, 24) (dual of [(13115, 5), 65372, 25]-NRT-code) | [i] | Truncation for OOAs | |
| 2 | Linear OOA(2204, 11247, F2, 6, 25) (dual of [(11247, 6), 67278, 26]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Linear OOA(2204, 11247, F2, 7, 25) (dual of [(11247, 7), 78525, 26]-NRT-code) | [i] | ||
| 4 | Linear OOA(2204, 11247, F2, 8, 25) (dual of [(11247, 8), 89772, 26]-NRT-code) | [i] | ||
| 5 | Digital (179, 204, 11247)-net over F2 | [i] | ||