Information on Result #674119
Linear OA(2114, 157, F2, 38) (dual of [157, 43, 39]-code), using construction X applied to C([1,42]) ⊂ C([1,28]) based on
- linear OA(298, 127, F2, 42) (dual of [127, 29, 43]-code), using the primitive narrow-sense BCH-code C(I) with length 127 = 27−1, defining interval I = [1,42], and designed minimum distance d ≥ |I|+1 = 43 [i]
- linear OA(284, 127, F2, 30) (dual of [127, 43, 31]-code), using the primitive narrow-sense BCH-code C(I) with length 127 = 27−1, defining interval I = [1,28], and minimum distance d ≥ 31 (sporadic result) [i]
- linear OA(216, 30, F2, 7) (dual of [30, 14, 8]-code), using
- discarding factors / shortening the dual code based on linear OA(216, 31, F2, 7) (dual of [31, 15, 8]-code), using
- code C0 for u = 5 by de Boer and Brouwer [i]
- discarding factors / shortening the dual code based on linear OA(216, 31, F2, 7) (dual of [31, 15, 8]-code), 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(2115, 158, F2, 39) (dual of [158, 43, 40]-code) | [i] | Adding a Parity Check Bit | |