Information on Result #630308
Linear OA(2128, 198, F2, 39) (dual of [198, 70, 40]-code), using concatenation of two codes based on
- linear OA(3219, 33, F32, 19) (dual of [33, 14, 20]-code or 33-arc in PG(18,32)), using
- extended Reed–Solomon code RSe(14,32) [i]
- the expurgated narrow-sense BCH-code C(I) with length 33 | 322−1, defining interval I = [0,9], and minimum distance d ≥ |{−9,−8,…,9}|+1 = 20 (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(2128, 198, F2, 38) (dual of [198, 70, 39]-code) | [i] | Strength Reduction | |
| 2 | Linear OA(2129, 199, F2, 39) (dual of [199, 70, 40]-code) | [i] | Code Embedding in Larger Space | |
| 3 | Linear OA(2130, 200, F2, 39) (dual of [200, 70, 40]-code) | [i] | ||
| 4 | Linear OA(2131, 201, F2, 39) (dual of [201, 70, 40]-code) | [i] | ||
| 5 | Linear OA(2132, 202, F2, 39) (dual of [202, 70, 40]-code) | [i] | ||
| 6 | Linear OA(2127, 197, F2, 38) (dual of [197, 70, 39]-code) | [i] | Truncation | |
| 7 | Linear OOA(2128, 99, F2, 2, 39) (dual of [(99, 2), 70, 40]-NRT-code) | [i] | OOA Folding | |
| 8 | Linear OOA(2128, 66, F2, 3, 39) (dual of [(66, 3), 70, 40]-NRT-code) | [i] | ||