Information on Result #2227477
Linear OA(329, 2195, F3, 6) (dual of [2195, 2166, 7]-code), using 1 times truncation based on linear OA(330, 2196, F3, 7) (dual of [2196, 2166, 8]-code), using
- construction X4 applied to Ce(6) ⊂ Ce(4) [i] based on
- linear OA(329, 2187, F3, 7) (dual of [2187, 2158, 8]-code), using an extension Ce(6) of the primitive narrow-sense BCH-code C(I) with length 2186 = 37−1, defining interval I = [1,6], and designed minimum distance d ≥ |I|+1 = 7 [i]
- linear OA(322, 2187, F3, 5) (dual of [2187, 2165, 6]-code), using an extension Ce(4) of the primitive narrow-sense BCH-code C(I) with length 2186 = 37−1, defining interval I = [1,4], and designed minimum distance d ≥ |I|+1 = 5 [i]
- linear OA(38, 9, F3, 8) (dual of [9, 1, 9]-code or 9-arc in PG(7,3)), using
- dual of repetition code with length 9 [i]
- linear OA(31, 9, F3, 1) (dual of [9, 8, 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(329, 2195, F3, 2, 6) (dual of [(2195, 2), 4361, 7]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(329, 2195, F3, 3, 6) (dual of [(2195, 3), 6556, 7]-NRT-code) | [i] | ||
| 3 | Linear OOA(329, 2195, F3, 4, 6) (dual of [(2195, 4), 8751, 7]-NRT-code) | [i] | ||
| 4 | Linear OOA(329, 2195, F3, 5, 6) (dual of [(2195, 5), 10946, 7]-NRT-code) | [i] | ||
| 5 | Linear OA(331, 2214, F3, 6) (dual of [2214, 2183, 7]-code) | [i] | Varšamov–Edel Lengthening | |
| 6 | Linear OOA(329, 1097, F3, 2, 6) (dual of [(1097, 2), 2165, 7]-NRT-code) | [i] | OOA Folding | |
| 7 | Linear OOA(329, 731, F3, 3, 6) (dual of [(731, 3), 2164, 7]-NRT-code) | [i] | ||
| 8 | Linear OOA(329, 731, F3, 4, 6) (dual of [(731, 4), 2895, 7]-NRT-code) | [i] | OA Folding and Stacking | |
| 9 | Linear OOA(329, 731, F3, 5, 6) (dual of [(731, 5), 3626, 7]-NRT-code) | [i] | ||