Information on Result #2277156
Linear OA(5106, 1953158, F5, 14) (dual of [1953158, 1953052, 15]-code), using 3 times code embedding in larger space based on linear OA(5103, 1953155, F5, 14) (dual of [1953155, 1953052, 15]-code), using
- construction X applied to Ce(13) ⊂ Ce(10) [i] based on
- linear OA(5100, 1953125, F5, 14) (dual of [1953125, 1953025, 15]-code), using an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 1953124 = 59−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [i]
- linear OA(573, 1953125, F5, 11) (dual of [1953125, 1953052, 12]-code), using an extension Ce(10) of the primitive narrow-sense BCH-code C(I) with length 1953124 = 59−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [i]
- linear OA(53, 30, F5, 2) (dual of [30, 27, 3]-code), using
- discarding factors / shortening the dual code based on linear OA(53, 31, F5, 2) (dual of [31, 28, 3]-code), using
- Hamming code H(3,5) [i]
- discarding factors / shortening the dual code based on linear OA(53, 31, F5, 2) (dual of [31, 28, 3]-code), 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(5106, 1726979, F5, 2, 14) (dual of [(1726979, 2), 3453852, 15]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(5106, 1726979, F5, 3, 14) (dual of [(1726979, 3), 5180831, 15]-NRT-code) | [i] | ||
| 3 | Digital (92, 106, 1726979)-net over F5 | [i] | ||