Information on Result #946566
Linear OOA(2141, 693, F2, 3, 25) (dual of [(693, 3), 1938, 26]-NRT-code), using OOA 3-folding based on linear OA(2141, 2079, F2, 25) (dual of [2079, 1938, 26]-code), using
- 2 times code embedding in larger space [i] based on linear OA(2139, 2077, F2, 25) (dual of [2077, 1938, 26]-code), using
- construction X applied to C([0,12]) ⊂ C([0,10]) [i] based on
- linear OA(2133, 2049, F2, 25) (dual of [2049, 1916, 26]-code), using the expurgated narrow-sense BCH-code C(I) with length 2049 | 222−1, defining interval I = [0,12], and minimum distance d ≥ |{−12,−11,…,12}|+1 = 26 (BCH-bound) [i]
- linear OA(2111, 2049, F2, 21) (dual of [2049, 1938, 22]-code), using the expurgated narrow-sense BCH-code C(I) with length 2049 | 222−1, defining interval I = [0,10], and minimum distance d ≥ |{−10,−9,…,10}|+1 = 22 (BCH-bound) [i]
- linear OA(26, 28, F2, 3) (dual of [28, 22, 4]-code or 28-cap in PG(5,2)), using
- discarding factors / shortening the dual code based on 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([0,12]) ⊂ 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(2141, 693, F2, 3, 24) (dual of [(693, 3), 1938, 25]-NRT-code) | [i] | Strength Reduction for OOAs | |
| 2 | Linear OOA(2142, 693, F2, 3, 25) (dual of [(693, 3), 1937, 26]-NRT-code) | [i] | OOA Duplication | |
| 3 | Linear OOA(2143, 693, F2, 3, 25) (dual of [(693, 3), 1936, 26]-NRT-code) | [i] | ||
| 4 | Linear OOA(2140, 692, F2, 3, 24) (dual of [(692, 3), 1936, 25]-NRT-code) | [i] | Truncation for OOAs | |
| 5 | Linear OOA(2141, 693, F2, 4, 25) (dual of [(693, 4), 2631, 26]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 6 | Linear OOA(2141, 693, F2, 5, 25) (dual of [(693, 5), 3324, 26]-NRT-code) | [i] | ||
| 7 | Linear OOA(2141, 693, F2, 6, 25) (dual of [(693, 6), 4017, 26]-NRT-code) | [i] | ||
| 8 | Linear OOA(2141, 693, F2, 7, 25) (dual of [(693, 7), 4710, 26]-NRT-code) | [i] | ||
| 9 | Linear OOA(2141, 693, F2, 8, 25) (dual of [(693, 8), 5403, 26]-NRT-code) | [i] | ||
| 10 | Digital (116, 141, 693)-net over F2 | [i] | ||