Information on Result #629398
Linear OA(2159, 171, F2, 75) (dual of [171, 12, 76]-code), using concatenation of two codes based on
- linear OA(451, 57, F4, 37) (dual of [57, 6, 38]-code), using
- discarding factors / shortening the dual code based on linear OA(451, 59, F4, 37) (dual of [59, 8, 38]-code), using
- 6 times truncation [i] based on linear OA(457, 65, F4, 43) (dual of [65, 8, 44]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 65 | 46−1, defining interval I = [0,21], and minimum distance d ≥ |{−21,−20,…,21}|+1 = 44 (BCH-bound) [i]
- 6 times truncation [i] based on linear OA(457, 65, F4, 43) (dual of [65, 8, 44]-code), using
- discarding factors / shortening the dual code based on linear OA(451, 59, F4, 37) (dual of [59, 8, 38]-code), using
- 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(2158, 170, F2, 74) (dual of [170, 12, 75]-code) | [i] | Truncation | |
| 2 | Linear OOA(2159, 57, F2, 3, 75) (dual of [(57, 3), 12, 76]-NRT-code) | [i] | OOA Folding | |
| 3 | Linear OOA(2159, 34, F2, 5, 75) (dual of [(34, 5), 11, 76]-NRT-code) | [i] | ||