Information on Result #678318
Linear OA(4119, 262191, F4, 17) (dual of [262191, 262072, 18]-code), using construction X applied to C([0,8]) ⊂ C([0,5]) based on
- linear OA(4109, 262145, F4, 17) (dual of [262145, 262036, 18]-code), using the expurgated narrow-sense BCH-code C(I) with length 262145 | 418−1, defining interval I = [0,8], and minimum distance d ≥ |{−8,−7,…,8}|+1 = 18 (BCH-bound) [i]
- linear OA(473, 262145, F4, 11) (dual of [262145, 262072, 12]-code), using the expurgated narrow-sense BCH-code C(I) with length 262145 | 418−1, defining interval I = [0,5], and minimum distance d ≥ |{−5,−4,…,5}|+1 = 12 (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(4120, 262192, F4, 17) (dual of [262192, 262072, 18]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OA(4118, 262190, F4, 16) (dual of [262190, 262072, 17]-code) | [i] | Truncation | |
| 3 | Linear OOA(4119, 131095, F4, 2, 17) (dual of [(131095, 2), 262071, 18]-NRT-code) | [i] | OOA Folding | |
| 4 | Linear OOA(4119, 87397, F4, 3, 17) (dual of [(87397, 3), 262072, 18]-NRT-code) | [i] | ||
| 5 | Linear OOA(4119, 32773, F4, 17, 17) (dual of [(32773, 17), 557022, 18]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |