Information on Result #682218
Linear OA(573, 1953135, F5, 10) (dual of [1953135, 1953062, 11]-code), using construction X4 applied to C([1,10]) ⊂ C([1,8]) based on
- linear OA(572, 1953124, F5, 10) (dual of [1953124, 1953052, 11]-code), using 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(563, 1953124, F5, 8) (dual of [1953124, 1953061, 9]-code), using the primitive narrow-sense BCH-code C(I) with length 1953124 = 59−1, defining interval I = [1,8], and designed minimum distance d ≥ |I|+1 = 9 [i]
- linear OA(510, 11, F5, 10) (dual of [11, 1, 11]-code or 11-arc in PG(9,5)), using
- dual of repetition code with length 11 [i]
- linear OA(51, 11, F5, 1) (dual of [11, 10, 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(573, 1838057, F5, 2, 10) (dual of [(1838057, 2), 3676041, 11]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(573, 1838057, F5, 3, 10) (dual of [(1838057, 3), 5514098, 11]-NRT-code) | [i] | ||
| 3 | Digital (63, 73, 1838057)-net over F5 | [i] | ||
| 4 | Linear OOA(573, 976567, F5, 2, 10) (dual of [(976567, 2), 1953061, 11]-NRT-code) | [i] | OOA Folding | |
| 5 | Linear OOA(573, 651045, F5, 3, 10) (dual of [(651045, 3), 1953062, 11]-NRT-code) | [i] | ||
| 6 | Linear OOA(573, 390627, F5, 10, 10) (dual of [(390627, 10), 3906197, 11]-NRT-code) | [i] | OA Folding and Stacking | |