Information on Result #681986
Linear OA(456, 83, F4, 27) (dual of [83, 27, 28]-code), using construction XX applied to C([0,80]) ⊂ C([0,65]) ⊂ C([1,62]) based on
- linear OA(447, 63, F4, 27) (dual of [63, 16, 28]-code), using contraction [i] based on linear OA(4173, 189, F4, 83) (dual of [189, 16, 84]-code), using the expurgated narrow-sense BCH-code C(I) with length 189 | 49−1, defining interval I = [0,80], and minimum distance d ≥ |{−2,−1,…,80}|+1 = 84 (BCH-bound) [i]
- linear OA(438, 63, F4, 22) (dual of [63, 25, 23]-code), using contraction [i] based on linear OA(4164, 189, F4, 68) (dual of [189, 25, 69]-code), using the expurgated narrow-sense BCH-code C(I) with length 189 | 49−1, defining interval I = [0,65], and minimum distance d ≥ |{−2,−1,…,65}|+1 = 69 (BCH-bound) [i]
- linear OA(436, 63, F4, 20) (dual of [63, 27, 21]-code), using contraction [i] based on linear OA(4162, 189, F4, 62) (dual of [189, 27, 63]-code), using the narrow-sense BCH-code C(I) with length 189 | 49−1, defining interval I = [1,62], and designed minimum distance d ≥ |I|+1 = 63 [i]
- linear OA(46, 17, F4, 4) (dual of [17, 11, 5]-code), using
- discarding factors / shortening the dual code based on linear OA(46, 21, F4, 4) (dual of [21, 15, 5]-code), using
- linear OA(41, 3, F4, 1) (dual of [3, 2, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(41, 4, F4, 1) (dual of [4, 3, 2]-code), using
- Reed–Solomon code RS(3,4) [i]
- discarding factors / shortening the dual code based on linear OA(41, 4, F4, 1) (dual of [4, 3, 2]-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.
Compare with Markus Grassl’s online database of code parameters.
Other Results with Identical Parameters
None.
Depending Results
The following results depend on this result:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | Linear OA(4138, 164, F4, 55) (dual of [164, 26, 56]-code) | [i] | Repeating Each Code Word | |
| 2 | Linear OA(4137, 162, F4, 55) (dual of [162, 25, 56]-code) | [i] | ||
| 3 | Linear OA(4136, 160, F4, 55) (dual of [160, 24, 56]-code) | [i] | ||
| 4 | Linear OA(4135, 158, F4, 55) (dual of [158, 23, 56]-code) | [i] | ||
| 5 | Linear OA(4134, 156, F4, 55) (dual of [156, 22, 56]-code) | [i] | ||
| 6 | Linear OA(4133, 154, F4, 55) (dual of [154, 21, 56]-code) | [i] | ||
| 7 | Linear OA(4132, 152, F4, 55) (dual of [152, 20, 56]-code) | [i] | ||
| 8 | Linear OA(4131, 150, F4, 55) (dual of [150, 19, 56]-code) | [i] | ||
| 9 | Linear OA(4130, 148, F4, 55) (dual of [148, 18, 56]-code) | [i] | ||