Information on Result #679513
Linear OA(4209, 4149, F4, 43) (dual of [4149, 3940, 44]-code), using construction X applied to C([0,21]) ⊂ C([0,17]) based on
- linear OA(4193, 4097, F4, 43) (dual of [4097, 3904, 44]-code), using the expurgated narrow-sense BCH-code C(I) with length 4097 | 412−1, defining interval I = [0,21], and minimum distance d ≥ |{−21,−20,…,21}|+1 = 44 (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(416, 52, F4, 7) (dual of [52, 36, 8]-code), using
- discarding factors / shortening the dual code based on linear OA(416, 63, F4, 7) (dual of [63, 47, 8]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 63 = 43−1, defining interval I = [0,6], and designed minimum distance d ≥ |I|+1 = 8 [i]
- discarding factors / shortening the dual code based on linear OA(416, 63, F4, 7) (dual of [63, 47, 8]-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(4210, 4150, F4, 43) (dual of [4150, 3940, 44]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OOA(4209, 2074, F4, 2, 43) (dual of [(2074, 2), 3939, 44]-NRT-code) | [i] | OOA Folding | |
| 3 | Linear OOA(4209, 1383, F4, 3, 43) (dual of [(1383, 3), 3940, 44]-NRT-code) | [i] | ||