Information on Result #700835
Linear OA(3112, 118, F3, 74) (dual of [118, 6, 75]-code), using construction XX applied to C({0,1,2,4,5,7,8,10,11,13,14,16,17,19,20,23,26,28,29,32,34,52,56,68}) ⊂ C([0,56]) ⊂ C([1,56]) based on
- linear OA(3102, 104, F3, 77) (dual of [104, 2, 78]-code), using the cyclic code C(A) with length 104 | 36−1, defining set A = {0,1,2,4,5,7,8,10,11,13,14,16,17,19,20,23,26,28,29,32,34,52,56,68}, and minimum distance d ≥ |{4,21,38,…,48}|+1 = 78 (BCH-bound) [i]
- linear OA(399, 104, F3, 68) (dual of [104, 5, 69]-code), using the expurgated narrow-sense BCH-code C(I) with length 104 | 36−1, defining interval I = [0,64], and minimum distance d ≥ |{−3,−2,…,64}|+1 = 69 (BCH-bound) [i]
- linear OA(398, 104, F3, 64) (dual of [104, 6, 65]-code), using the narrow-sense BCH-code C(I) with length 104 | 36−1, defining interval I = [1,64], and designed minimum distance d ≥ |I|+1 = 65 [i]
- linear OA(36, 10, F3, 5) (dual of [10, 4, 6]-code), using
- linear OA(33, 4, F3, 3) (dual of [4, 1, 4]-code or 4-arc in PG(2,3) or 4-cap in PG(2,3)), using
- dual of repetition code with length 4 [i]
- oval in PG(2, 3) [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(3112, 59, F3, 2, 74) (dual of [(59, 2), 6, 75]-NRT-code) | [i] | OOA Folding | |