Information on Result #683457
Linear OA(534, 630, F5, 11) (dual of [630, 596, 12]-code), using construction X applied to Ce(10) ⊂ Ce(8) based on
- linear OA(533, 625, F5, 11) (dual of [625, 592, 12]-code), using an extension Ce(10) of the primitive narrow-sense BCH-code C(I) with length 624 = 54−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [i]
- linear OA(529, 625, F5, 9) (dual of [625, 596, 10]-code), using an extension Ce(8) of the primitive narrow-sense BCH-code C(I) with length 624 = 54−1, defining interval I = [1,8], and designed minimum distance d ≥ |I|+1 = 9 [i]
- linear OA(51, 5, F5, 1) (dual of [5, 4, 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(534, 373, F5, 2, 11) (dual of [(373, 2), 712, 12]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(534, 373, F5, 3, 11) (dual of [(373, 3), 1085, 12]-NRT-code) | [i] | ||
| 3 | Digital (23, 34, 373)-net over F5 | [i] | ||
| 4 | Linear OA(537, 643, F5, 11) (dual of [643, 606, 12]-code) | [i] | Varšamov–Edel Lengthening | |
| 5 | Linear OOA(534, 315, F5, 2, 11) (dual of [(315, 2), 596, 12]-NRT-code) | [i] | OOA Folding | |
| 6 | Linear OOA(534, 210, F5, 3, 11) (dual of [(210, 3), 596, 12]-NRT-code) | [i] | ||