Information on Result #684407
Linear OA(523, 36, F5, 13) (dual of [36, 13, 14]-code), using construction XX applied to C1 = C([0,10]), C2 = C([1,11]), C3 = C1 + C2 = C([1,10]), and C∩ = C1 ∩ C2 = C([0,11]) based on
- 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(521, 31, F5, 11) (dual of [31, 10, 12]-code), using the narrow-sense BCH-code C(I) with length 31 | 53−1, defining interval I = [1,11], and designed minimum distance d ≥ |I|+1 = 12 [i]
- linear OA(522, 31, F5, 13) (dual of [31, 9, 14]-code), using the expurgated narrow-sense BCH-code C(I) with length 31 | 53−1, defining interval I = [0,11], and minimum distance d ≥ |{−1,0,…,11}|+1 = 14 (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(51, 2, F5, 1) (dual of [2, 1, 2]-code), using
- dual of repetition code with length 2 [i]
- linear OA(50, 3, F5, 0) (dual of [3, 3, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(50, s, F5, 0) (dual of [s, s, 1]-code) for arbitrarily large s, 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 OOA(523, 18, F5, 2, 13) (dual of [(18, 2), 13, 14]-NRT-code) | [i] | OOA Folding | |