Information on Result #629423
Linear OA(2174, 186, F2, 85) (dual of [186, 12, 86]-code), using concatenation of two codes based on
- linear OA(456, 62, F4, 42) (dual of [62, 6, 43]-code), using
- discarding factors / shortening the dual code based on linear OA(456, 63, F4, 42) (dual of [63, 7, 43]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 63 = 43−1, defining interval I = [0,31], and designed minimum distance d ≥ |I|+1 = 43 [i]
- discarding factors / shortening the dual code based on linear OA(456, 63, F4, 42) (dual of [63, 7, 43]-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(2173, 185, F2, 84) (dual of [185, 12, 85]-code) | [i] | Truncation | |
| 2 | Linear OA(2205, 216, F2, 96) (dual of [216, 11, 97]-code) | [i] | Juxtaposition | |
| 3 | Linear OOA(2174, 93, F2, 2, 85) (dual of [(93, 2), 12, 86]-NRT-code) | [i] | OOA Folding | |
| 4 | Linear OOA(2174, 62, F2, 3, 85) (dual of [(62, 3), 12, 86]-NRT-code) | [i] | ||
| 5 | Linear OOA(2174, 37, F2, 5, 85) (dual of [(37, 5), 11, 86]-NRT-code) | [i] | ||