Information on Result #682855
Linear OA(551, 15634, F5, 11) (dual of [15634, 15583, 12]-code), using construction XX applied to Ce(10) ⊂ Ce(8) ⊂ Ce(7) based on
- linear OA(549, 15625, F5, 11) (dual of [15625, 15576, 12]-code), using an extension Ce(10) of the primitive narrow-sense BCH-code C(I) with length 15624 = 56−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [i]
- linear OA(543, 15625, F5, 9) (dual of [15625, 15582, 10]-code), using an extension Ce(8) of the primitive narrow-sense BCH-code C(I) with length 15624 = 56−1, defining interval I = [1,8], and designed minimum distance d ≥ |I|+1 = 9 [i]
- linear OA(537, 15625, F5, 8) (dual of [15625, 15588, 9]-code), using an extension Ce(7) of the primitive narrow-sense BCH-code C(I) with length 15624 = 56−1, defining interval I = [1,7], and designed minimum distance d ≥ |I|+1 = 8 [i]
- linear OA(51, 8, F5, 1) (dual of [8, 7, 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
- linear OA(50, 1, F5, 0) (dual of [1, 1, 1]-code), using
- dual of repetition code with length 1 [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 OOA(551, 7917, F5, 2, 11) (dual of [(7917, 2), 15783, 12]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(551, 7917, F5, 3, 11) (dual of [(7917, 3), 23700, 12]-NRT-code) | [i] | ||
| 3 | Digital (40, 51, 7917)-net over F5 | [i] | ||
| 4 | Linear OOA(551, 7817, F5, 2, 11) (dual of [(7817, 2), 15583, 12]-NRT-code) | [i] | OOA Folding | |
| 5 | Linear OOA(551, 5211, F5, 3, 11) (dual of [(5211, 3), 15582, 12]-NRT-code) | [i] | ||