Information on Result #675506
Linear OA(334, 6579, F3, 6) (dual of [6579, 6545, 7]-code), using construction X4 applied to Ce(6) ⊂ Ce(3) based on
- linear OA(333, 6561, F3, 7) (dual of [6561, 6528, 8]-code), using an extension Ce(6) of the primitive narrow-sense BCH-code C(I) with length 6560 = 38−1, defining interval I = [1,6], and designed minimum distance d ≥ |I|+1 = 7 [i]
- linear OA(317, 6561, F3, 4) (dual of [6561, 6544, 5]-code), using an extension Ce(3) of the primitive narrow-sense BCH-code C(I) with length 6560 = 38−1, defining interval I = [1,3], and designed minimum distance d ≥ |I|+1 = 4 [i]
- linear OA(317, 18, F3, 17) (dual of [18, 1, 18]-code or 18-arc in PG(16,3)), using
- dual of repetition code with length 18 [i]
- linear OA(31, 18, F3, 1) (dual of [18, 17, 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(334, 6579, F3, 2, 6) (dual of [(6579, 2), 13124, 7]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(334, 6579, F3, 3, 6) (dual of [(6579, 3), 19703, 7]-NRT-code) | [i] | ||
| 3 | Linear OOA(334, 6579, F3, 4, 6) (dual of [(6579, 4), 26282, 7]-NRT-code) | [i] | ||
| 4 | Linear OOA(334, 6579, F3, 5, 6) (dual of [(6579, 5), 32861, 7]-NRT-code) | [i] | ||
| 5 | Linear OOA(334, 2193, F3, 3, 6) (dual of [(2193, 3), 6545, 7]-NRT-code) | [i] | OOA Folding | |
| 6 | Linear OOA(334, 2193, F3, 4, 6) (dual of [(2193, 4), 8738, 7]-NRT-code) | [i] | OA Folding and Stacking | |
| 7 | Linear OOA(334, 2193, F3, 5, 6) (dual of [(2193, 5), 10931, 7]-NRT-code) | [i] | ||