Information on Result #677619
Linear OA(371, 87, F3, 42) (dual of [87, 16, 43]-code), using construction XX applied to C([1,87]) ⊂ C([1,81]) ⊂ C([1,79]) based on
- linear OA(369, 80, F3, 43) (dual of [80, 11, 44]-code), using contraction [i] based on linear OA(3149, 160, F3, 87) (dual of [160, 11, 88]-code), using the narrow-sense BCH-code C(I) with length 160 | 38−1, defining interval I = [1,87], and designed minimum distance d ≥ |I|+1 = 88 [i]
- linear OA(365, 80, F3, 40) (dual of [80, 15, 41]-code), using contraction [i] based on linear OA(3145, 160, F3, 81) (dual of [160, 15, 82]-code), using the narrow-sense BCH-code C(I) with length 160 | 38−1, defining interval I = [1,81], and designed minimum distance d ≥ |I|+1 = 82 [i]
- linear OA(364, 80, F3, 39) (dual of [80, 16, 40]-code), using contraction [i] based on linear OA(3144, 160, F3, 79) (dual of [160, 16, 80]-code), using the narrow-sense BCH-code C(I) with length 160 | 38−1, defining interval I = [1,79], and designed minimum distance d ≥ |I|+1 = 80 [i]
- linear OA(31, 6, F3, 1) (dual of [6, 5, 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.
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(371, 87, F3, 41) (dual of [87, 16, 42]-code) | [i] | Strength Reduction | |
| 2 | Linear OA(371, 87, F3, 40) (dual of [87, 16, 41]-code) | [i] | ||
| 3 | Linear OA(371, 87, F3, 39) (dual of [87, 16, 40]-code) | [i] | ||
| 4 | Linear OA(371, 87, F3, 38) (dual of [87, 16, 39]-code) | [i] | ||
| 5 | Linear OA(371, 87, F3, 37) (dual of [87, 16, 38]-code) | [i] | ||
| 6 | Linear OA(371, 87, F3, 36) (dual of [87, 16, 37]-code) | [i] | ||
| 7 | Linear OA(380, 97, F3, 42) (dual of [97, 17, 43]-code) | [i] | Construction X with Varšamov Bound | |
| 8 | Linear OOA(371, 29, F3, 3, 42) (dual of [(29, 3), 16, 43]-NRT-code) | [i] | OOA Folding | |