Information on Result #1053786
Linear OOA(2212, 2052, F2, 4, 32) (dual of [(2052, 4), 7996, 33]-NRT-code), using OOA 4-folding based on linear OA(2212, 8208, F2, 32) (dual of [8208, 7996, 33]-code), using
- 3 times code embedding in larger space [i] based on linear OA(2209, 8205, F2, 32) (dual of [8205, 7996, 33]-code), using
- 1 times truncation [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
- 1 times truncation [i] based on linear OA(2210, 8206, F2, 33) (dual of [8206, 7996, 34]-code), using
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, 32) (dual of [(2052, 4), 7995, 33]-NRT-code) | [i] | OOA Duplication | |
| 2 | Linear OOA(2212, 2052, F2, 5, 32) (dual of [(2052, 5), 10048, 33]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Linear OOA(2212, 2052, F2, 6, 32) (dual of [(2052, 6), 12100, 33]-NRT-code) | [i] | ||
| 4 | Linear OOA(2212, 2052, F2, 7, 32) (dual of [(2052, 7), 14152, 33]-NRT-code) | [i] | ||
| 5 | Linear OOA(2212, 2052, F2, 8, 32) (dual of [(2052, 8), 16204, 33]-NRT-code) | [i] | ||
| 6 | Digital (180, 212, 2052)-net over F2 | [i] | ||