Information on Result #737292
Linear OA(4190, 4130, F4, 41) (dual of [4130, 3940, 42]-code), using construction X applied to C([0,20]) ⊂ C([0,17]) based on
- linear OA(4181, 4097, F4, 41) (dual of [4097, 3916, 42]-code), using the expurgated narrow-sense BCH-code C(I) with length 4097 | 412−1, defining interval I = [0,20], and minimum distance d ≥ |{−20,−19,…,20}|+1 = 42 (BCH-bound) [i]
- linear OA(4157, 4097, F4, 35) (dual of [4097, 3940, 36]-code), using the expurgated narrow-sense BCH-code C(I) with length 4097 | 412−1, defining interval I = [0,17], and minimum distance d ≥ |{−17,−16,…,17}|+1 = 36 (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(4192, 4132, F4, 41) (dual of [4132, 3940, 42]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OA(4193, 4133, F4, 41) (dual of [4133, 3940, 42]-code) | [i] | ||
| 3 | Linear OA(4189, 4129, F4, 40) (dual of [4129, 3940, 41]-code) | [i] | Truncation | |
| 4 | Linear OA(4191, 4132, F4, 41) (dual of [4132, 3941, 42]-code) | [i] | Construction X with Varšamov Bound | |
| 5 | Linear OA(4192, 4134, F4, 41) (dual of [4134, 3942, 42]-code) | [i] | ||
| 6 | Linear OOA(4190, 2065, F4, 2, 41) (dual of [(2065, 2), 3940, 42]-NRT-code) | [i] | OOA Folding | |
| 7 | Linear OOA(4190, 1376, F4, 3, 41) (dual of [(1376, 3), 3938, 42]-NRT-code) | [i] | ||