Information on Result #2272300
Linear OA(4138, 16424, F4, 25) (dual of [16424, 16286, 26]-code), using 1 times code embedding in larger space based on linear OA(4137, 16423, F4, 25) (dual of [16423, 16286, 26]-code), using
- construction X applied to C([0,12]) ⊂ C([0,9]) [i] based on
- linear OA(4127, 16385, F4, 25) (dual of [16385, 16258, 26]-code), using the expurgated narrow-sense BCH-code C(I) with length 16385 | 414−1, defining interval I = [0,12], and minimum distance d ≥ |{−12,−11,…,12}|+1 = 26 (BCH-bound) [i]
- linear OA(499, 16385, F4, 19) (dual of [16385, 16286, 20]-code), using the expurgated narrow-sense BCH-code C(I) with length 16385 | 414−1, defining interval I = [0,9], and minimum distance d ≥ |{−9,−8,…,9}|+1 = 20 (BCH-bound) [i]
- linear OA(410, 38, F4, 5) (dual of [38, 28, 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 OOA(4138, 12102, F4, 2, 25) (dual of [(12102, 2), 24066, 26]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(4138, 12102, F4, 3, 25) (dual of [(12102, 3), 36168, 26]-NRT-code) | [i] | ||
| 3 | Digital (113, 138, 12102)-net over F4 | [i] | ||
| 4 | Linear OOA(4138, 8212, F4, 2, 25) (dual of [(8212, 2), 16286, 26]-NRT-code) | [i] | OOA Folding | |