Information on Result #675938
Linear OA(3198, 2202, F3, 42) (dual of [2202, 2004, 43]-code), using construction X applied to Ce(42) ⊂ Ce(39) based on
- linear OA(3197, 2187, F3, 43) (dual of [2187, 1990, 44]-code), using an extension Ce(42) of the primitive narrow-sense BCH-code C(I) with length 2186 = 37−1, defining interval I = [1,42], and designed minimum distance d ≥ |I|+1 = 43 [i]
- linear OA(3183, 2187, F3, 40) (dual of [2187, 2004, 41]-code), using an extension Ce(39) of the primitive narrow-sense BCH-code C(I) with length 2186 = 37−1, defining interval I = [1,39], and designed minimum distance d ≥ |I|+1 = 40 [i]
- linear OA(31, 15, F3, 1) (dual of [15, 14, 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 OA(3199, 2203, F3, 42) (dual of [2203, 2004, 43]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OOA(3198, 1727, F3, 2, 42) (dual of [(1727, 2), 3256, 43]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Linear OOA(3198, 1727, F3, 3, 42) (dual of [(1727, 3), 4983, 43]-NRT-code) | [i] | ||
| 4 | Linear OOA(3198, 1727, F3, 4, 42) (dual of [(1727, 4), 6710, 43]-NRT-code) | [i] | ||
| 5 | Linear OOA(3198, 1727, F3, 5, 42) (dual of [(1727, 5), 8437, 43]-NRT-code) | [i] | ||
| 6 | Digital (156, 198, 1727)-net over F3 | [i] | ||
| 7 | Linear OA(3206, 2232, F3, 42) (dual of [2232, 2026, 43]-code) | [i] | Varšamov–Edel Lengthening | |
| 8 | Linear OA(3207, 2245, F3, 42) (dual of [2245, 2038, 43]-code) | [i] | ||
| 9 | Linear OA(3208, 2263, F3, 42) (dual of [2263, 2055, 43]-code) | [i] | ||
| 10 | Linear OA(3209, 2288, F3, 42) (dual of [2288, 2079, 43]-code) | [i] | ||
| 11 | Linear OA(3210, 2319, F3, 42) (dual of [2319, 2109, 43]-code) | [i] | ||
| 12 | Linear OA(3211, 2359, F3, 42) (dual of [2359, 2148, 43]-code) | [i] | ||
| 13 | Linear OA(3212, 2407, F3, 42) (dual of [2407, 2195, 43]-code) | [i] | ||
| 14 | Linear OA(3213, 2461, F3, 42) (dual of [2461, 2248, 43]-code) | [i] | ||
| 15 | Linear OA(3214, 2522, F3, 42) (dual of [2522, 2308, 43]-code) | [i] | ||
| 16 | Linear OA(3215, 2587, F3, 42) (dual of [2587, 2372, 43]-code) | [i] | ||
| 17 | Linear OOA(3198, 1101, F3, 2, 42) (dual of [(1101, 2), 2004, 43]-NRT-code) | [i] | OOA Folding | |
| 18 | Linear OOA(3198, 734, F3, 3, 42) (dual of [(734, 3), 2004, 43]-NRT-code) | [i] | ||
| 19 | Linear OOA(3198, 550, F3, 4, 42) (dual of [(550, 4), 2002, 43]-NRT-code) | [i] | ||
| 20 | Linear OOA(3198, 440, F3, 5, 42) (dual of [(440, 5), 2002, 43]-NRT-code) | [i] | ||