Information on Result #2281294
Linear OA(8123, 262159, F8, 23) (dual of [262159, 262036, 24]-code), using 1 times code embedding in larger space based on linear OA(8122, 262158, F8, 23) (dual of [262158, 262036, 24]-code), using
- construction X applied to C([0,11]) ⊂ C([0,10]) [i] based on
- linear OA(8121, 262145, F8, 23) (dual of [262145, 262024, 24]-code), using the expurgated narrow-sense BCH-code C(I) with length 262145 | 812−1, defining interval I = [0,11], and minimum distance d ≥ |{−11,−10,…,11}|+1 = 24 (BCH-bound) [i]
- linear OA(8109, 262145, F8, 21) (dual of [262145, 262036, 22]-code), using the expurgated narrow-sense BCH-code C(I) with length 262145 | 812−1, defining interval I = [0,10], and minimum distance d ≥ |{−10,−9,…,10}|+1 = 22 (BCH-bound) [i]
- linear OA(81, 13, F8, 1) (dual of [13, 12, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(81, s, F8, 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 OOA(8123, 218722, F8, 2, 23) (dual of [(218722, 2), 437321, 24]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(8123, 218722, F8, 3, 23) (dual of [(218722, 3), 656043, 24]-NRT-code) | [i] | ||
| 3 | Digital (100, 123, 218722)-net over F8 | [i] | ||