Information on Result #629546
Linear OA(2178, 232, F2, 57) (dual of [232, 54, 58]-code), using concatenation of two codes based on
- linear OA(840, 58, F8, 28) (dual of [58, 18, 29]-code), using
- discarding factors / shortening the dual code based on linear OA(840, 63, F8, 28) (dual of [63, 23, 29]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 63 = 82−1, defining interval I = [0,27], and designed minimum distance d ≥ |I|+1 = 29 [i]
- discarding factors / shortening the dual code based on linear OA(840, 63, F8, 28) (dual of [63, 23, 29]-code), using
- linear OA(21, 4, F2, 1) (dual of [4, 3, 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(2177, 231, F2, 56) (dual of [231, 54, 57]-code) | [i] | Truncation | |
| 2 | Linear OOA(2178, 116, F2, 2, 57) (dual of [(116, 2), 54, 58]-NRT-code) | [i] | OOA Folding | |
| 3 | Linear OOA(2178, 77, F2, 3, 57) (dual of [(77, 3), 53, 58]-NRT-code) | [i] | ||