Information on Result #2175000
Linear OA(2129, 145, F2, 57) (dual of [145, 16, 58]-code), using adding a parity check bit based on linear OA(2128, 144, F2, 56) (dual of [144, 16, 57]-code), using
- construction XX applied toD3 ⊂ D2 ⊂ D1 [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(2105, 127, F2, 46) (dual of [127, 22, 47]-code), using augmented code D1 for u = 7 by de Boer and Brouwer [i]
- linear OA(21, 9, F2, 1) (dual of [9, 8, 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
- linear OA(27, 8, F2, 7) (dual of [8, 1, 8]-code or 8-arc in PG(6,2)), using
- dual of repetition code with length 8 [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(2129, 145, F2, 56) (dual of [145, 16, 57]-code) | [i] | Strength Reduction | |
| 2 | Linear OA(2130, 146, F2, 57) (dual of [146, 16, 58]-code) | [i] | Code Embedding in Larger Space | |
| 3 | Linear OOA(2129, 29, F2, 5, 57) (dual of [(29, 5), 16, 58]-NRT-code) | [i] | OOA Folding | |