Information on Result #692843
Linear OA(1694, 273, F16, 51) (dual of [273, 179, 52]-code), using construction X applied to Ce(50) ⊂ Ce(42) based on
- linear OA(1687, 256, F16, 51) (dual of [256, 169, 52]-code), using an extension Ce(50) of the primitive narrow-sense BCH-code C(I) with length 255 = 162−1, defining interval I = [1,50], and designed minimum distance d ≥ |I|+1 = 51 [i]
- linear OA(1677, 256, F16, 43) (dual of [256, 179, 44]-code), using an extension Ce(42) of the primitive narrow-sense BCH-code C(I) with length 255 = 162−1, defining interval I = [1,42], and designed minimum distance d ≥ |I|+1 = 43 [i]
- linear OA(167, 17, F16, 7) (dual of [17, 10, 8]-code or 17-arc in PG(6,16)), using
- extended Reed–Solomon code RSe(10,16) [i]
- the expurgated narrow-sense BCH-code C(I) with length 17 | 162−1, defining interval I = [0,3], and minimum distance d ≥ |{−3,−2,…,3}|+1 = 8 (BCH-bound) [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.
Other Results with Identical Parameters
None.
Depending Results
The following results depend on this result:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | Linear OA(1695, 274, F16, 51) (dual of [274, 179, 52]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OA(1693, 272, F16, 50) (dual of [272, 179, 51]-code) | [i] | Truncation | |
| 3 | Linear OA(1692, 271, F16, 49) (dual of [271, 179, 50]-code) | [i] | ||
| 4 | Linear OOA(1694, 136, F16, 2, 51) (dual of [(136, 2), 178, 52]-NRT-code) | [i] | OOA Folding | |