Information on Result #2226312
Linear OA(2181, 4108, F2, 30) (dual of [4108, 3927, 31]-code), using 1 times truncation based on linear OA(2182, 4109, F2, 31) (dual of [4109, 3927, 32]-code), using
- construction X applied to Ce(30) ⊂ Ce(28) [i] based on
- linear OA(2181, 4096, F2, 31) (dual of [4096, 3915, 32]-code), using an extension Ce(30) of the primitive narrow-sense BCH-code C(I) with length 4095 = 212−1, defining interval I = [1,30], and designed minimum distance d ≥ |I|+1 = 31 [i]
- linear OA(2169, 4096, F2, 29) (dual of [4096, 3927, 30]-code), using an extension Ce(28) of the primitive narrow-sense BCH-code C(I) with length 4095 = 212−1, defining interval I = [1,28], and designed minimum distance d ≥ |I|+1 = 29 [i]
- linear OA(21, 13, F2, 1) (dual of [13, 12, 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
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 OA(2183, 4110, F2, 30) (dual of [4110, 3927, 31]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OA(2184, 4111, F2, 30) (dual of [4111, 3927, 31]-code) | [i] | ||
| 3 | Linear OA(2185, 4112, F2, 30) (dual of [4112, 3927, 31]-code) | [i] | ||
| 4 | Linear OOA(2181, 2054, F2, 2, 30) (dual of [(2054, 2), 3927, 31]-NRT-code) | [i] | OOA Folding | |
| 5 | Linear OOA(2181, 1369, F2, 3, 30) (dual of [(1369, 3), 3926, 31]-NRT-code) | [i] | ||
| 6 | Linear OOA(2181, 1027, F2, 4, 30) (dual of [(1027, 4), 3927, 31]-NRT-code) | [i] | ||
| 7 | Linear OOA(2181, 821, F2, 5, 30) (dual of [(821, 5), 3924, 31]-NRT-code) | [i] | ||
| 8 | Linear OOA(2181, 684, F2, 6, 30) (dual of [(684, 6), 3923, 31]-NRT-code) | [i] | ||
| 9 | Linear OOA(2181, 586, F2, 7, 30) (dual of [(586, 7), 3921, 31]-NRT-code) | [i] | ||
| 10 | Linear OOA(2181, 513, F2, 8, 30) (dual of [(513, 8), 3923, 31]-NRT-code) | [i] | ||