Information on Result #631041
Linear OA(3189, 231, F3, 81) (dual of [231, 42, 82]-code), using concatenation of two codes based on
- linear OA(956, 77, F9, 40) (dual of [77, 21, 41]-code), using
- discarding factors / shortening the dual code based on linear OA(956, 80, F9, 40) (dual of [80, 24, 41]-code), using
- the primitive narrow-sense BCH-code C(I) with length 80 = 92−1, defining interval I = [1,40], and designed minimum distance d ≥ |I|+1 = 41 [i]
- the primitive expurgated narrow-sense BCH-code C(I) with length 80 = 92−1, defining interval I = [0,39], and designed minimum distance d ≥ |I|+1 = 41 [i]
- discarding factors / shortening the dual code based on linear OA(956, 80, F9, 40) (dual of [80, 24, 41]-code), using
- linear OA(31, 3, F3, 1) (dual of [3, 2, 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.
Compare with Markus Grassl’s online database of code parameters.
Other Results with Identical Parameters
None.
Depending Results
The following results depend on this result:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | Linear OA(3188, 230, F3, 80) (dual of [230, 42, 81]-code) | [i] | Truncation | |
| 2 | Linear OOA(3189, 115, F3, 2, 81) (dual of [(115, 2), 41, 82]-NRT-code) | [i] | OOA Folding | |
| 3 | Linear OOA(3189, 77, F3, 3, 81) (dual of [(77, 3), 42, 82]-NRT-code) | [i] | ||