Information on Result #630312
Linear OA(2138, 198, F2, 43) (dual of [198, 60, 44]-code), using concatenation of two codes based on
- linear OA(3221, 33, F32, 21) (dual of [33, 12, 22]-code or 33-arc in PG(20,32)), using
- extended Reed–Solomon code RSe(12,32) [i]
- the expurgated narrow-sense BCH-code C(I) with length 33 | 322−1, defining interval I = [0,10], and minimum distance d ≥ |{−10,−9,…,10}|+1 = 22 (BCH-bound) [i]
- linear OA(21, 6, F2, 1) (dual of [6, 5, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(21, s, F2, 1) (dual of [s, s−1, 2]-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 OA(2138, 198, F2, 42) (dual of [198, 60, 43]-code) | [i] | Strength Reduction | |
| 2 | Linear OA(2139, 199, F2, 43) (dual of [199, 60, 44]-code) | [i] | Code Embedding in Larger Space | |
| 3 | Linear OA(2137, 197, F2, 42) (dual of [197, 60, 43]-code) | [i] | Truncation | |
| 4 | Linear OOA(2138, 99, F2, 2, 43) (dual of [(99, 2), 60, 44]-NRT-code) | [i] | OOA Folding | |
| 5 | Linear OOA(2138, 66, F2, 3, 43) (dual of [(66, 3), 60, 44]-NRT-code) | [i] | ||