Information on Result #674133
Linear OA(230, 137, F2, 8) (dual of [137, 107, 9]-code), using construction X4 applied to C([0,8]) ⊂ C([1,6]) based on
- linear OA(229, 127, F2, 9) (dual of [127, 98, 10]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 127 = 27−1, defining interval I = [0,8], and designed minimum distance d ≥ |I|+1 = 10 [i]
- linear OA(221, 127, F2, 6) (dual of [127, 106, 7]-code), using the primitive narrow-sense BCH-code C(I) with length 127 = 27−1, defining interval I = [1,6], and designed minimum distance d ≥ |I|+1 = 7 [i]
- linear OA(29, 10, F2, 9) (dual of [10, 1, 10]-code or 10-arc in PG(8,2)), using
- dual of repetition code with length 10 [i]
- linear OA(21, 10, F2, 1) (dual of [10, 9, 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 OOA(230, 78, F2, 2, 8) (dual of [(78, 2), 126, 9]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(230, 78, F2, 3, 8) (dual of [(78, 3), 204, 9]-NRT-code) | [i] | ||
| 3 | Linear OOA(230, 78, F2, 4, 8) (dual of [(78, 4), 282, 9]-NRT-code) | [i] | ||
| 4 | Linear OOA(230, 78, F2, 5, 8) (dual of [(78, 5), 360, 9]-NRT-code) | [i] | ||
| 5 | Linear OOA(230, 78, F2, 6, 8) (dual of [(78, 6), 438, 9]-NRT-code) | [i] | ||
| 6 | Linear OOA(230, 78, F2, 7, 8) (dual of [(78, 7), 516, 9]-NRT-code) | [i] | ||