Information on Result #672788
Linear OA(293, 8207, F2, 14) (dual of [8207, 8114, 15]-code), using construction X4 applied to C([0,14]) ⊂ C([1,12]) based on
- linear OA(292, 8191, F2, 15) (dual of [8191, 8099, 16]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 8191 = 213−1, defining interval I = [0,14], and designed minimum distance d ≥ |I|+1 = 16 [i]
- linear OA(278, 8191, F2, 12) (dual of [8191, 8113, 13]-code), using the primitive narrow-sense BCH-code C(I) with length 8191 = 213−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
- linear OA(215, 16, F2, 15) (dual of [16, 1, 16]-code or 16-arc in PG(14,2)), using
- dual of repetition code with length 16 [i]
- linear OA(21, 16, F2, 1) (dual of [16, 15, 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.
Other Results with Identical Parameters
None.
Depending Results
The following results depend on this result:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | Linear OA(295, 8209, F2, 14) (dual of [8209, 8114, 15]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OA(296, 8210, F2, 14) (dual of [8210, 8114, 15]-code) | [i] | ||
| 3 | Linear OA(294, 8208, F2, 15) (dual of [8208, 8114, 16]-code) | [i] | Adding a Parity Check Bit | |
| 4 | Linear OOA(293, 4103, F2, 2, 14) (dual of [(4103, 2), 8113, 15]-NRT-code) | [i] | OOA Folding | |