Information on Result #679527
Linear OA(4161, 4149, F4, 33) (dual of [4149, 3988, 34]-code), using construction X applied to C([0,16]) ⊂ C([0,12]) 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(4109, 4097, F4, 25) (dual of [4097, 3988, 26]-code), using the expurgated narrow-sense BCH-code C(I) with length 4097 | 412−1, defining interval I = [0,12], and minimum distance d ≥ |{−12,−11,…,12}|+1 = 26 (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(4161, 4149, F4, 32) (dual of [4149, 3988, 33]-code) | [i] | Strength Reduction | |
| 2 | Linear OA(4162, 4150, F4, 33) (dual of [4150, 3988, 34]-code) | [i] | Code Embedding in Larger Space | |
| 3 | Linear OA(4163, 4151, F4, 33) (dual of [4151, 3988, 34]-code) | [i] | ||
| 4 | Linear OA(4160, 4148, F4, 32) (dual of [4148, 3988, 33]-code) | [i] | Truncation | |
| 5 | Linear OOA(4161, 2074, F4, 2, 33) (dual of [(2074, 2), 3987, 34]-NRT-code) | [i] | OOA Folding | |
| 6 | Linear OOA(4161, 1383, F4, 3, 33) (dual of [(1383, 3), 3988, 34]-NRT-code) | [i] | ||