Information on Result #709973
Linear OA(580, 159, F5, 32) (dual of [159, 79, 33]-code), using construction XX applied to C1 = C([1,30]), C2 = C([13,32]), C3 = C1 + C2 = C([13,30]), and C∩ = C1 ∩ C2 = C([1,32]) based on
- linear OA(560, 124, F5, 30) (dual of [124, 64, 31]-code), using the primitive narrow-sense BCH-code C(I) with length 124 = 53−1, defining interval I = [1,30], and designed minimum distance d ≥ |I|+1 = 31 [i]
- linear OA(549, 124, F5, 20) (dual of [124, 75, 21]-code), using the primitive BCH-code C(I) with length 124 = 53−1, defining interval I = {13,14,…,32}, and designed minimum distance d ≥ |I|+1 = 21 [i]
- linear OA(564, 124, F5, 32) (dual of [124, 60, 33]-code), using the primitive narrow-sense BCH-code C(I) with length 124 = 53−1, defining interval I = [1,32], and designed minimum distance d ≥ |I|+1 = 33 [i]
- linear OA(545, 124, F5, 18) (dual of [124, 79, 19]-code), using the primitive BCH-code C(I) with length 124 = 53−1, defining interval I = {13,14,…,30}, and designed minimum distance d ≥ |I|+1 = 19 [i]
- linear OA(515, 30, F5, 11) (dual of [30, 15, 12]-code), using
- extended quadratic residue code Qe(30,5) [i]
- linear OA(51, 5, F5, 1) (dual of [5, 4, 2]-code), using
- Reed–Solomon code RS(4,5) [i]
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(581, 160, F5, 32) (dual of [160, 79, 33]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OA(579, 158, F5, 31) (dual of [158, 79, 32]-code) | [i] | Truncation | |
| 3 | Linear OOA(580, 79, F5, 2, 32) (dual of [(79, 2), 78, 33]-NRT-code) | [i] | OOA Folding | |