Information on Result #678306
Linear OA(4227, 262191, F4, 33) (dual of [262191, 261964, 34]-code), using construction X applied to C([0,16]) ⊂ C([0,13]) based on
- linear OA(4217, 262145, F4, 33) (dual of [262145, 261928, 34]-code), using the expurgated narrow-sense BCH-code C(I) with length 262145 | 418−1, defining interval I = [0,16], and minimum distance d ≥ |{−16,−15,…,16}|+1 = 34 (BCH-bound) [i]
- linear OA(4181, 262145, F4, 27) (dual of [262145, 261964, 28]-code), using the expurgated narrow-sense BCH-code C(I) with length 262145 | 418−1, defining interval I = [0,13], and minimum distance d ≥ |{−13,−12,…,13}|+1 = 28 (BCH-bound) [i]
- linear OA(410, 46, F4, 5) (dual of [46, 36, 6]-code), using
- discarding factors / shortening the dual code based on linear OA(410, 63, F4, 5) (dual of [63, 53, 6]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 63 = 43−1, defining interval I = [0,3], and designed minimum distance d ≥ |I|+1 = 6 [i]
- discarding factors / shortening the dual code based on linear OA(410, 63, F4, 5) (dual of [63, 53, 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(4228, 262192, F4, 33) (dual of [262192, 261964, 34]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OA(4229, 262193, F4, 33) (dual of [262193, 261964, 34]-code) | [i] | ||
| 3 | Linear OA(4226, 262190, F4, 32) (dual of [262190, 261964, 33]-code) | [i] | Truncation | |
| 4 | Linear OOA(4227, 131095, F4, 2, 33) (dual of [(131095, 2), 261963, 34]-NRT-code) | [i] | OOA Folding | |
| 5 | Linear OOA(4227, 87397, F4, 3, 33) (dual of [(87397, 3), 261964, 34]-NRT-code) | [i] | ||