Information on Result #2272948
Linear OA(4204, 65580, F4, 33) (dual of [65580, 65376, 34]-code), using 1 times code embedding in larger space based on linear OA(4203, 65579, F4, 33) (dual of [65579, 65376, 34]-code), using
- construction X applied to C([0,16]) ⊂ C([0,13]) [i] based on
- linear OA(4193, 65537, F4, 33) (dual of [65537, 65344, 34]-code), using the expurgated narrow-sense BCH-code C(I) with length 65537 | 416−1, defining interval I = [0,16], and minimum distance d ≥ |{−16,−15,…,16}|+1 = 34 (BCH-bound) [i]
- linear OA(4161, 65537, F4, 27) (dual of [65537, 65376, 28]-code), using the expurgated narrow-sense BCH-code C(I) with length 65537 | 416−1, defining interval I = [0,13], and minimum distance d ≥ |{−13,−12,…,13}|+1 = 28 (BCH-bound) [i]
- linear OA(410, 42, F4, 5) (dual of [42, 32, 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(4204, 36236, F4, 2, 33) (dual of [(36236, 2), 72268, 34]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(4204, 36236, F4, 3, 33) (dual of [(36236, 3), 108504, 34]-NRT-code) | [i] | ||
| 3 | Digital (171, 204, 36236)-net over F4 | [i] | ||
| 4 | Linear OOA(4204, 32790, F4, 2, 33) (dual of [(32790, 2), 65376, 34]-NRT-code) | [i] | OOA Folding | |
| 5 | Linear OOA(4204, 21860, F4, 3, 33) (dual of [(21860, 3), 65376, 34]-NRT-code) | [i] | ||