Information on Result #629417
Linear OA(2172, 186, F2, 83) (dual of [186, 14, 84]-code), using concatenation of two codes based on
- linear OA(455, 62, F4, 41) (dual of [62, 7, 42]-code), using
- discarding factors / shortening the dual code based on linear OA(455, 63, F4, 41) (dual of [63, 8, 42]-code), using
- 2 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]
- 2 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(455, 63, F4, 41) (dual of [63, 8, 42]-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(2171, 185, F2, 82) (dual of [185, 14, 83]-code) | [i] | Truncation | |
| 2 | Linear OOA(2172, 93, F2, 2, 83) (dual of [(93, 2), 14, 84]-NRT-code) | [i] | OOA Folding | |
| 3 | Linear OOA(2172, 62, F2, 3, 83) (dual of [(62, 3), 14, 84]-NRT-code) | [i] | ||
| 4 | Linear OOA(2172, 37, F2, 5, 83) (dual of [(37, 5), 13, 84]-NRT-code) | [i] | ||