Information on Result #2227630
Linear OA(333, 6570, F3, 6) (dual of [6570, 6537, 7]-code), using 1 times truncation based on linear OA(334, 6571, F3, 7) (dual of [6571, 6537, 8]-code), using
- construction X4 applied to Ce(6) ⊂ Ce(4) [i] 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(325, 6561, F3, 5) (dual of [6561, 6536, 6]-code), using an extension Ce(4) of the primitive narrow-sense BCH-code C(I) with length 6560 = 38−1, defining interval I = [1,4], and designed minimum distance d ≥ |I|+1 = 5 [i]
- linear OA(39, 10, F3, 9) (dual of [10, 1, 10]-code or 10-arc in PG(8,3)), using
- dual of repetition code with length 10 [i]
- linear OA(31, 10, F3, 1) (dual of [10, 9, 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(333, 6570, F3, 2, 6) (dual of [(6570, 2), 13107, 7]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(333, 6570, F3, 3, 6) (dual of [(6570, 3), 19677, 7]-NRT-code) | [i] | ||
| 3 | Linear OOA(333, 6570, F3, 4, 6) (dual of [(6570, 4), 26247, 7]-NRT-code) | [i] | ||
| 4 | Linear OOA(333, 6570, F3, 5, 6) (dual of [(6570, 5), 32817, 7]-NRT-code) | [i] | ||
| 5 | Linear OOA(333, 3285, F3, 2, 6) (dual of [(3285, 2), 6537, 7]-NRT-code) | [i] | OOA Folding | |
| 6 | Linear OOA(333, 2190, F3, 3, 6) (dual of [(2190, 3), 6537, 7]-NRT-code) | [i] | ||
| 7 | Linear OOA(333, 2190, F3, 4, 6) (dual of [(2190, 4), 8727, 7]-NRT-code) | [i] | OA Folding and Stacking | |
| 8 | Linear OOA(333, 2190, F3, 5, 6) (dual of [(2190, 5), 10917, 7]-NRT-code) | [i] | ||