Information on Result #701241
Linear OA(537, 71, F5, 17) (dual of [71, 34, 18]-code), using construction XX applied to C1 = C({0,1,2,3,4,6,7,8,9,11,37}), C2 = C([0,12]), C3 = C1 + C2 = C([0,11]), and C∩ = C1 ∩ C2 = C({0,1,2,3,4,6,7,8,9,11,12,37}) based on
- linear OA(531, 62, F5, 13) (dual of [62, 31, 14]-code), using the cyclic code C(A) with length 62 | 53−1, defining set A = {0,1,2,3,4,6,7,8,9,11,37}, and minimum distance d ≥ |{−1,0,…,11}|+1 = 14 (BCH-bound) [i]
- linear OA(531, 62, F5, 16) (dual of [62, 31, 17]-code), using the expurgated narrow-sense BCH-code C(I) with length 62 | 53−1, defining interval I = [0,12], and designed minimum distance d ≥ |I|+1 = 17 [i]
- linear OA(534, 62, F5, 18) (dual of [62, 28, 19]-code), using the cyclic code C(A) with length 62 | 53−1, defining set A = {0,1,2,3,4,6,7,8,9,11,12,37}, and minimum distance d ≥ |{−2,−1,…,15}|+1 = 19 (BCH-bound) [i]
- linear OA(528, 62, F5, 12) (dual of [62, 34, 13]-code), using the expurgated narrow-sense BCH-code C(I) with length 62 | 53−1, defining interval I = [0,11], and designed minimum distance d ≥ |I|+1 = 13 [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
- linear OA(53, 6, F5, 3) (dual of [6, 3, 4]-code or 6-arc in PG(2,5) or 6-cap in PG(2,5)), using
- extended Reed–Solomon code RSe(3,5) [i]
- oval in PG(2, 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 OOA(537, 35, F5, 2, 17) (dual of [(35, 2), 33, 18]-NRT-code) | [i] | OOA Folding | |