Information on Result #674113
Linear OA(2119, 159, F2, 42) (dual of [159, 40, 43]-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(221, 32, F2, 11) (dual of [32, 11, 12]-code), using
- an extension Ce(10) of the primitive narrow-sense BCH-code C(I) with length 31 = 25−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [i]
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(2120, 160, F2, 43) (dual of [160, 40, 44]-code) | [i] | Adding a Parity Check Bit | |
| 2 | Linear OOA(2119, 79, F2, 2, 42) (dual of [(79, 2), 39, 43]-NRT-code) | [i] | OOA Folding | |
| 3 | Linear OOA(2119, 53, F2, 3, 42) (dual of [(53, 3), 40, 43]-NRT-code) | [i] | ||