Information on Result #2174977
Linear OA(2121, 136, F2, 57) (dual of [136, 15, 58]-code), using adding a parity check bit based on linear OA(2120, 135, F2, 56) (dual of [135, 15, 57]-code), using
- construction X applied to D3 ⊂ D2 [i] based on
- linear OA(2119, 127, F2, 58) (dual of [127, 8, 59]-code), using augmented code D3 for u = 7 by de Boer and Brouwer [i]
- linear OA(2112, 127, F2, 54) (dual of [127, 15, 55]-code), using augmented code D2 for u = 7 by de Boer and Brouwer [i]
- linear OA(21, 8, F2, 1) (dual of [8, 7, 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(2121, 136, F2, 56) (dual of [136, 15, 57]-code) | [i] | Strength Reduction | |
| 2 | Linear OA(2122, 137, F2, 57) (dual of [137, 15, 58]-code) | [i] | Code Embedding in Larger Space | |
| 3 | Linear OA(2119, 134, F2, 55) (dual of [134, 15, 56]-code) | [i] | Truncation | |
| 4 | Linear OA(2118, 133, F2, 54) (dual of [133, 15, 55]-code) | [i] | ||
| 5 | Linear OA(2117, 132, F2, 53) (dual of [132, 15, 54]-code) | [i] | ||
| 6 | Linear OA(2116, 131, F2, 52) (dual of [131, 15, 53]-code) | [i] | ||
| 7 | Linear OA(264, 78, F2, 28) (dual of [78, 14, 29]-code) | [i] | Residual Code | |
| 8 | Linear OOA(2121, 68, F2, 2, 57) (dual of [(68, 2), 15, 58]-NRT-code) | [i] | OOA Folding | |