Information on Result #737293
Linear OA(4154, 4130, F4, 33) (dual of [4130, 3976, 34]-code), using construction X applied to C([0,16]) ⊂ C([0,13]) based on
- linear OA(4145, 4097, F4, 33) (dual of [4097, 3952, 34]-code), using the expurgated narrow-sense BCH-code C(I) with length 4097 | 412−1, defining interval I = [0,16], and minimum distance d ≥ |{−16,−15,…,16}|+1 = 34 (BCH-bound) [i]
- linear OA(4121, 4097, F4, 27) (dual of [4097, 3976, 28]-code), using the expurgated narrow-sense BCH-code C(I) with length 4097 | 412−1, defining interval I = [0,13], and minimum distance d ≥ |{−13,−12,…,13}|+1 = 28 (BCH-bound) [i]
- linear OA(49, 33, F4, 5) (dual of [33, 24, 6]-code), using
- discarding factors / shortening the dual code based on linear OA(49, 36, F4, 5) (dual of [36, 27, 6]-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 OA(4156, 4132, F4, 33) (dual of [4132, 3976, 34]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OA(4157, 4133, F4, 33) (dual of [4133, 3976, 34]-code) | [i] | ||
| 3 | Linear OA(4153, 4129, F4, 32) (dual of [4129, 3976, 33]-code) | [i] | Truncation | |
| 4 | Linear OA(4156, 4133, F4, 33) (dual of [4133, 3977, 34]-code) | [i] | Construction X with Varšamov Bound | |
| 5 | Linear OA(4157, 4135, F4, 33) (dual of [4135, 3978, 34]-code) | [i] | ||
| 6 | Linear OOA(4154, 2065, F4, 2, 33) (dual of [(2065, 2), 3976, 34]-NRT-code) | [i] | OOA Folding | |
| 7 | Linear OOA(4154, 1376, F4, 3, 33) (dual of [(1376, 3), 3974, 34]-NRT-code) | [i] | ||