Information on Result #737522
Linear OA(564, 78160, F5, 11) (dual of [78160, 78096, 12]-code), using construction X applied to Ce(10) ⊂ Ce(5) based on
- linear OA(557, 78125, F5, 11) (dual of [78125, 78068, 12]-code), using an extension Ce(10) of the primitive narrow-sense BCH-code C(I) with length 78124 = 57−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [i]
- linear OA(529, 78125, F5, 6) (dual of [78125, 78096, 7]-code), using an extension Ce(5) of the primitive narrow-sense BCH-code C(I) with length 78124 = 57−1, defining interval I = [1,5], and designed minimum distance d ≥ |I|+1 = 6 [i]
- linear OA(57, 35, F5, 4) (dual of [35, 28, 5]-code), using
- discarding factors / shortening the dual code based on linear OA(57, 44, F5, 4) (dual of [44, 37, 5]-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 OA(563, 78159, F5, 10) (dual of [78159, 78096, 11]-code) | [i] | Truncation | |
| 2 | Linear OOA(564, 78160, F5, 2, 11) (dual of [(78160, 2), 156256, 12]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Linear OOA(564, 78160, F5, 3, 11) (dual of [(78160, 3), 234416, 12]-NRT-code) | [i] | ||
| 4 | Digital (53, 64, 78160)-net over F5 | [i] | ||
| 5 | Linear OOA(564, 39080, F5, 2, 11) (dual of [(39080, 2), 78096, 12]-NRT-code) | [i] | OOA Folding | |
| 6 | Linear OOA(564, 26053, F5, 3, 11) (dual of [(26053, 3), 78095, 12]-NRT-code) | [i] | ||
| 7 | Linear OOA(564, 15631, F5, 11, 11) (dual of [(15631, 11), 171877, 12]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |