Information on Result #2245494
Linear OA(529, 78133, F5, 5) (dual of [78133, 78104, 6]-code), using 1 times truncation based on linear OA(530, 78134, F5, 6) (dual of [78134, 78104, 7]-code), using
- construction X4 applied to Ce(5) ⊂ Ce(3) [i] based on
- 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(522, 78125, F5, 4) (dual of [78125, 78103, 5]-code), using an extension Ce(3) of the primitive narrow-sense BCH-code C(I) with length 78124 = 57−1, defining interval I = [1,3], and designed minimum distance d ≥ |I|+1 = 4 [i]
- linear OA(58, 9, F5, 8) (dual of [9, 1, 9]-code or 9-arc in PG(7,5)), using
- dual of repetition code with length 9 [i]
- linear OA(51, 9, F5, 1) (dual of [9, 8, 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(529, 78133, F5, 2, 5) (dual of [(78133, 2), 156237, 6]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(529, 78133, F5, 3, 5) (dual of [(78133, 3), 234370, 6]-NRT-code) | [i] | ||
| 3 | Digital (24, 29, 78133)-net over F5 | [i] | ||
| 4 | Linear OOA(529, 39066, F5, 2, 5) (dual of [(39066, 2), 78103, 6]-NRT-code) | [i] | OOA Folding | |
| 5 | Linear OOA(529, 39066, F5, 3, 5) (dual of [(39066, 3), 117169, 6]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |
| 6 | Linear OOA(529, 39066, F5, 5, 5) (dual of [(39066, 5), 195301, 6]-NRT-code) | [i] | ||