Information on Result #1053883
Linear OOA(2210, 2051, F2, 4, 33) (dual of [(2051, 4), 7994, 34]-NRT-code), using OOA 4-folding based on linear OA(2210, 8204, F2, 33) (dual of [8204, 7994, 34]-code), using
- discarding factors / shortening the dual code 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(2210, 2051, F2, 4, 32) (dual of [(2051, 4), 7994, 33]-NRT-code) | [i] | Strength Reduction for OOAs | |
| 2 | Linear OOA(2211, 2051, F2, 4, 33) (dual of [(2051, 4), 7993, 34]-NRT-code) | [i] | OOA Duplication | |
| 3 | Linear OOA(2210, 1812, F2, 5, 33) (dual of [(1812, 5), 8850, 34]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 4 | Linear OOA(2210, 1812, F2, 6, 33) (dual of [(1812, 6), 10662, 34]-NRT-code) | [i] | ||
| 5 | Linear OOA(2210, 1812, F2, 7, 33) (dual of [(1812, 7), 12474, 34]-NRT-code) | [i] | ||
| 6 | Linear OOA(2210, 1812, F2, 8, 33) (dual of [(1812, 8), 14286, 34]-NRT-code) | [i] | ||
| 7 | Digital (177, 210, 1812)-net over F2 | [i] | ||