Information on Result #686025
Linear OA(731, 60, F7, 17) (dual of [60, 29, 18]-code), using construction X applied to C([0,8]) ⊂ C([0,5]) based on
- linear OA(725, 50, F7, 17) (dual of [50, 25, 18]-code), using the expurgated narrow-sense BCH-code C(I) with length 50 | 74−1, defining interval I = [0,8], and minimum distance d ≥ |{−8,−7,…,8}|+1 = 18 (BCH-bound) [i]
- linear OA(721, 50, F7, 11) (dual of [50, 29, 12]-code), using the expurgated narrow-sense BCH-code C(I) with length 50 | 74−1, defining interval I = [0,5], and minimum distance d ≥ |{−5,−4,…,5}|+1 = 12 (BCH-bound) [i]
- linear OA(76, 10, F7, 5) (dual of [10, 4, 6]-code), using
- construction X applied to C([0,2]) ⊂ C([1,2]) [i] based on
- linear OA(75, 8, F7, 5) (dual of [8, 3, 6]-code or 8-arc in PG(4,7)), using the expurgated narrow-sense BCH-code C(I) with length 8 | 72−1, defining interval I = [0,2], and minimum distance d ≥ |{−2,−1,0,1,2}|+1 = 6 (BCH-bound) [i]
- linear OA(74, 8, F7, 3) (dual of [8, 4, 4]-code or 8-cap in PG(3,7)), using the narrow-sense BCH-code C(I) with length 8 | 72−1, defining interval I = [1,2], and minimum distance d ≥ |{1,2}| + |{−3,0}| = 4 (simple Roos-bound) [i]
- linear OA(71, 2, F7, 1) (dual of [2, 1, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(71, s, F7, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
- construction X applied to C([0,2]) ⊂ C([1,2]) [i] based on
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(731, 20, F7, 3, 17) (dual of [(20, 3), 29, 18]-NRT-code) | [i] | OOA Folding | |