Information on Result #629428
Linear OA(2177, 189, F2, 87) (dual of [189, 12, 88]-code), using concatenation of two codes based on
- linear OA(457, 63, F4, 43) (dual of [63, 6, 44]-code), using
- contraction [i] based on linear OA(4183, 189, F4, 131) (dual of [189, 6, 132]-code), using the expurgated narrow-sense BCH-code C(I) with length 189 | 49−1, defining interval I = [0,128], and minimum distance d ≥ |{−2,−1,…,128}|+1 = 132 (BCH-bound) [i]
- linear OA(21, 3, F2, 1) (dual of [3, 2, 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(2176, 188, F2, 86) (dual of [188, 12, 87]-code) | [i] | Truncation | |
| 2 | Linear OA(290, 101, F2, 43) (dual of [101, 11, 44]-code) | [i] | Residual Code | |
| 3 | Linear OOA(2177, 63, F2, 3, 87) (dual of [(63, 3), 12, 88]-NRT-code) | [i] | OOA Folding | |