Information on Result #674013
Linear OA(2129, 158, F2, 51) (dual of [158, 29, 52]-code), using construction X applied to Ce(54) ⊂ Ce(42) based on
- linear OA(2113, 128, F2, 55) (dual of [128, 15, 56]-code), using an extension Ce(54) of the primitive narrow-sense BCH-code C(I) with length 127 = 27−1, defining interval I = [1,54], and designed minimum distance d ≥ |I|+1 = 55 [i]
- linear OA(299, 128, F2, 43) (dual of [128, 29, 44]-code), using an extension Ce(42) of 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(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(2129, 158, F2, 50) (dual of [158, 29, 51]-code) | [i] | Strength Reduction | |
| 2 | Linear OA(2129, 158, F2, 49) (dual of [158, 29, 50]-code) | [i] | ||
| 3 | Linear OA(2129, 158, F2, 48) (dual of [158, 29, 49]-code) | [i] | ||
| 4 | Linear OA(2128, 157, F2, 50) (dual of [157, 29, 51]-code) | [i] | Truncation | |
| 5 | Linear OA(2127, 156, F2, 49) (dual of [156, 29, 50]-code) | [i] | ||