Information on Result #2273813
Linear OA(4257, 16430, F4, 47) (dual of [16430, 16173, 48]-code), using 1 times code embedding in larger space based on linear OA(4256, 16429, F4, 47) (dual of [16429, 16173, 48]-code), using
- construction X applied to Ce(46) ⊂ Ce(40) [i] based on
- linear OA(4246, 16384, F4, 47) (dual of [16384, 16138, 48]-code), using an extension Ce(46) of the primitive narrow-sense BCH-code C(I) with length 16383 = 47−1, defining interval I = [1,46], and designed minimum distance d ≥ |I|+1 = 47 [i]
- linear OA(4211, 16384, F4, 41) (dual of [16384, 16173, 42]-code), using an extension Ce(40) of the primitive narrow-sense BCH-code C(I) with length 16383 = 47−1, defining interval I = [1,40], and designed minimum distance d ≥ |I|+1 = 41 [i]
- linear OA(410, 45, F4, 5) (dual of [45, 35, 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(4257, 15599, F4, 2, 47) (dual of [(15599, 2), 30941, 48]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(4257, 15599, F4, 3, 47) (dual of [(15599, 3), 46540, 48]-NRT-code) | [i] | ||
| 3 | Digital (210, 257, 15599)-net over F4 | [i] | ||
| 4 | Linear OOA(4257, 8215, F4, 2, 47) (dual of [(8215, 2), 16173, 48]-NRT-code) | [i] | OOA Folding | |