Information on Result #2277445
Linear OA(5130, 78143, F5, 23) (dual of [78143, 78013, 24]-code), using 2 times code embedding in larger space based on linear OA(5128, 78141, F5, 23) (dual of [78141, 78013, 24]-code), using
- construction X applied to C([0,11]) ⊂ C([0,10]) [i] based on
- linear OA(5127, 78126, F5, 23) (dual of [78126, 77999, 24]-code), using the expurgated narrow-sense BCH-code C(I) with length 78126 | 514−1, defining interval I = [0,11], and minimum distance d ≥ |{−11,−10,…,11}|+1 = 24 (BCH-bound) [i]
- linear OA(5113, 78126, F5, 21) (dual of [78126, 78013, 22]-code), using the expurgated narrow-sense BCH-code C(I) with length 78126 | 514−1, defining interval I = [0,10], and minimum distance d ≥ |{−10,−9,…,10}|+1 = 22 (BCH-bound) [i]
- linear OA(51, 15, F5, 1) (dual of [15, 14, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(51, s, F5, 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(5130, 42654, F5, 2, 23) (dual of [(42654, 2), 85178, 24]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(5130, 42654, F5, 3, 23) (dual of [(42654, 3), 127832, 24]-NRT-code) | [i] | ||
| 3 | Digital (107, 130, 42654)-net over F5 | [i] | ||