Information on Result #1053884
Linear OOA(2212, 2052, F2, 4, 33) (dual of [(2052, 4), 7996, 34]-NRT-code), using OOA 4-folding based on linear OA(2212, 8208, F2, 33) (dual of [8208, 7996, 34]-code), using
- 2 times code embedding in larger space [i] based on linear OA(2210, 8206, F2, 33) (dual of [8206, 7996, 34]-code), using
- construction X applied to Ce(32) ⊂ Ce(30) [i] based on
- linear OA(2209, 8192, F2, 33) (dual of [8192, 7983, 34]-code), using an extension Ce(32) of the primitive narrow-sense BCH-code C(I) with length 8191 = 213−1, defining interval I = [1,32], and designed minimum distance d ≥ |I|+1 = 33 [i]
- linear OA(2196, 8192, F2, 31) (dual of [8192, 7996, 32]-code), using an extension Ce(30) of the primitive narrow-sense BCH-code C(I) with length 8191 = 213−1, defining interval I = [1,30], and designed minimum distance d ≥ |I|+1 = 31 [i]
- linear OA(21, 14, F2, 1) (dual of [14, 13, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(21, s, F2, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
- construction X applied to Ce(32) ⊂ Ce(30) [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(2213, 2052, F2, 4, 33) (dual of [(2052, 4), 7995, 34]-NRT-code) | [i] | OOA Duplication | |
| 2 | Linear OOA(2214, 2052, F2, 4, 33) (dual of [(2052, 4), 7994, 34]-NRT-code) | [i] | ||
| 3 | Linear OOA(2211, 2051, F2, 4, 32) (dual of [(2051, 4), 7993, 33]-NRT-code) | [i] | Truncation for OOAs | |
| 4 | Linear OOA(2212, 1906, F2, 5, 33) (dual of [(1906, 5), 9318, 34]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 5 | Linear OOA(2212, 1906, F2, 6, 33) (dual of [(1906, 6), 11224, 34]-NRT-code) | [i] | ||
| 6 | Linear OOA(2212, 1906, F2, 7, 33) (dual of [(1906, 7), 13130, 34]-NRT-code) | [i] | ||
| 7 | Linear OOA(2212, 1906, F2, 8, 33) (dual of [(1906, 8), 15036, 34]-NRT-code) | [i] | ||
| 8 | Digital (179, 212, 1906)-net over F2 | [i] | ||