Information on Result #684409
Linear OA(522, 38, F5, 12) (dual of [38, 16, 13]-code), using construction XX applied to C1 = C([0,7]), C2 = C([1,10]), C3 = C1 + C2 = C([1,7]), and C∩ = C1 ∩ C2 = C([0,10]) based on
- linear OA(516, 31, F5, 9) (dual of [31, 15, 10]-code), using the expurgated narrow-sense BCH-code C(I) with length 31 | 53−1, defining interval I = [0,7], and minimum distance d ≥ |{−1,0,…,7}|+1 = 10 (BCH-bound) [i]
- linear OA(518, 31, F5, 10) (dual of [31, 13, 11]-code), using the narrow-sense BCH-code C(I) with length 31 | 53−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [i]
- linear OA(519, 31, F5, 12) (dual of [31, 12, 13]-code), using the expurgated narrow-sense BCH-code C(I) with length 31 | 53−1, defining interval I = [0,10], and minimum distance d ≥ |{−1,0,…,10}|+1 = 13 (BCH-bound) [i]
- linear OA(515, 31, F5, 7) (dual of [31, 16, 8]-code), using the narrow-sense BCH-code C(I) with length 31 | 53−1, defining interval I = [1,7], and designed minimum distance d ≥ |I|+1 = 8 [i]
- linear OA(51, 2, F5, 1) (dual of [2, 1, 2]-code), using
- dual of repetition code with length 2 [i]
- linear OA(52, 5, F5, 2) (dual of [5, 3, 3]-code or 5-arc in PG(1,5)), using
- Reed–Solomon code RS(3,5) [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.
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(523, 42, F5, 12) (dual of [42, 19, 13]-code) | [i] | Varšamov–Edel Lengthening | |
| 2 | Linear OOA(522, 19, F5, 2, 12) (dual of [(19, 2), 16, 13]-NRT-code) | [i] | OOA Folding | |