Information on Result #678996
Linear OA(4182, 16440, F4, 32) (dual of [16440, 16258, 33]-code), using construction X applied to C([0,16]) ⊂ C([0,12]) based on
- linear OA(4169, 16385, F4, 33) (dual of [16385, 16216, 34]-code), using the expurgated narrow-sense BCH-code C(I) with length 16385 | 414−1, defining interval I = [0,16], and minimum distance d ≥ |{−16,−15,…,16}|+1 = 34 (BCH-bound) [i]
- 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(413, 55, F4, 6) (dual of [55, 42, 7]-code), using
- discarding factors / shortening the dual code based on linear OA(413, 63, F4, 6) (dual of [63, 50, 7]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 63 = 43−1, defining interval I = [0,5], and designed minimum distance d ≥ |I|+1 = 7 [i]
- discarding factors / shortening the dual code based on linear OA(413, 63, F4, 6) (dual of [63, 50, 7]-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(4183, 16441, F4, 32) (dual of [16441, 16258, 33]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OA(4186, 16444, F4, 32) (dual of [16444, 16258, 33]-code) | [i] | ||
| 3 | Linear OOA(4182, 16440, F4, 2, 32) (dual of [(16440, 2), 32698, 33]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 4 | Linear OOA(4182, 16440, F4, 3, 32) (dual of [(16440, 3), 49138, 33]-NRT-code) | [i] | ||
| 5 | Digital (150, 182, 16440)-net over F4 | [i] | ||
| 6 | Linear OA(4183, 16442, F4, 32) (dual of [16442, 16259, 33]-code) | [i] | Construction X with Varšamov Bound | |
| 7 | Linear OA(4184, 16444, F4, 32) (dual of [16444, 16260, 33]-code) | [i] | ||
| 8 | Linear OA(4185, 16446, F4, 32) (dual of [16446, 16261, 33]-code) | [i] | ||
| 9 | Linear OOA(4182, 8220, F4, 2, 32) (dual of [(8220, 2), 16258, 33]-NRT-code) | [i] | OOA Folding | |
| 10 | Linear OOA(4182, 5480, F4, 3, 32) (dual of [(5480, 3), 16258, 33]-NRT-code) | [i] | ||