Information on Result #676155
Linear OA(3213, 2197, F3, 46) (dual of [2197, 1984, 47]-code), using construction XX applied to Ce(45) ⊂ Ce(43) ⊂ Ce(42) based on
- linear OA(3211, 2187, F3, 46) (dual of [2187, 1976, 47]-code), using an extension Ce(45) of the primitive narrow-sense BCH-code C(I) with length 2186 = 37−1, defining interval I = [1,45], and designed minimum distance d ≥ |I|+1 = 46 [i]
- linear OA(3204, 2187, F3, 44) (dual of [2187, 1983, 45]-code), using an extension Ce(43) of the primitive narrow-sense BCH-code C(I) with length 2186 = 37−1, defining interval I = [1,43], and designed minimum distance d ≥ |I|+1 = 44 [i]
- 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(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
- linear OA(30, 1, F3, 0) (dual of [1, 1, 1]-code), using
- dual of repetition code with length 1 [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(3213, 1677, F3, 2, 46) (dual of [(1677, 2), 3141, 47]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(3213, 1677, F3, 3, 46) (dual of [(1677, 3), 4818, 47]-NRT-code) | [i] | ||
| 3 | Linear OOA(3213, 1677, F3, 4, 46) (dual of [(1677, 4), 6495, 47]-NRT-code) | [i] | ||
| 4 | Linear OOA(3213, 1677, F3, 5, 46) (dual of [(1677, 5), 8172, 47]-NRT-code) | [i] | ||
| 5 | Digital (167, 213, 1677)-net over F3 | [i] | ||
| 6 | Linear OOA(3213, 1098, F3, 2, 46) (dual of [(1098, 2), 1983, 47]-NRT-code) | [i] | OOA Folding | |
| 7 | Linear OOA(3213, 732, F3, 3, 46) (dual of [(732, 3), 1983, 47]-NRT-code) | [i] | ||
| 8 | Linear OOA(3213, 549, F3, 4, 46) (dual of [(549, 4), 1983, 47]-NRT-code) | [i] | ||