Information on Result #676256
Linear OA(338, 2197, F3, 8) (dual of [2197, 2159, 9]-code), using construction XX applied to Ce(7) ⊂ Ce(6) ⊂ Ce(4) based on
- linear OA(336, 2187, F3, 8) (dual of [2187, 2151, 9]-code), using an extension Ce(7) of the primitive narrow-sense BCH-code C(I) with length 2186 = 37−1, defining interval I = [1,7], and designed minimum distance d ≥ |I|+1 = 8 [i]
- 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(30, 8, F3, 0) (dual of [8, 8, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(30, s, F3, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
- linear OA(31, 2, F3, 1) (dual of [2, 1, 2]-code), using
- dual of repetition code with length 2 [i]
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(338, 1306, F3, 2, 8) (dual of [(1306, 2), 2574, 9]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(338, 1306, F3, 3, 8) (dual of [(1306, 3), 3880, 9]-NRT-code) | [i] | ||
| 3 | Linear OOA(338, 1306, F3, 4, 8) (dual of [(1306, 4), 5186, 9]-NRT-code) | [i] | ||
| 4 | Linear OOA(338, 1306, F3, 5, 8) (dual of [(1306, 5), 6492, 9]-NRT-code) | [i] | ||
| 5 | Digital (30, 38, 1306)-net over F3 | [i] | ||