Information on Result #674885
Linear OA(332, 59061, F3, 5) (dual of [59061, 59029, 6]-code), using construction X4 applied to Ce(4) ⊂ Ce(3) based on
- linear OA(331, 59049, F3, 5) (dual of [59049, 59018, 6]-code), using an extension Ce(4) of the primitive narrow-sense BCH-code C(I) with length 59048 = 310−1, defining interval I = [1,4], and designed minimum distance d ≥ |I|+1 = 5 [i]
- linear OA(321, 59049, F3, 4) (dual of [59049, 59028, 5]-code), using an extension Ce(3) of the primitive narrow-sense BCH-code C(I) with length 59048 = 310−1, defining interval I = [1,3], and designed minimum distance d ≥ |I|+1 = 4 [i]
- linear OA(311, 12, F3, 11) (dual of [12, 1, 12]-code or 12-arc in PG(10,3)), using
- dual of repetition code with length 12 [i]
- linear OA(31, 12, F3, 1) (dual of [12, 11, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(31, s, F3, 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(332, 59061, F3, 2, 5) (dual of [(59061, 2), 118090, 6]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(332, 59061, F3, 3, 5) (dual of [(59061, 3), 177151, 6]-NRT-code) | [i] | ||
| 3 | Linear OOA(332, 59061, F3, 4, 5) (dual of [(59061, 4), 236212, 6]-NRT-code) | [i] | ||
| 4 | Linear OOA(332, 29530, F3, 2, 5) (dual of [(29530, 2), 59028, 6]-NRT-code) | [i] | OOA Folding | |
| 5 | Linear OOA(332, 29530, F3, 3, 5) (dual of [(29530, 3), 88558, 6]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |
| 6 | Linear OOA(332, 29530, F3, 4, 5) (dual of [(29530, 4), 118088, 6]-NRT-code) | [i] | ||
| 7 | Linear OOA(332, 29530, F3, 5, 5) (dual of [(29530, 5), 147618, 6]-NRT-code) | [i] | ||