Information on Result #677809
Linear OA(325, 32, F3, 16) (dual of [32, 7, 17]-code), using construction XX applied to C([0,33]) ⊂ C([0,27]) ⊂ C([0,25]) based on
- linear OA(323, 26, F3, 17) (dual of [26, 3, 18]-code), using contraction [i] based on linear OA(349, 52, F3, 35) (dual of [52, 3, 36]-code), using the expurgated narrow-sense BCH-code C(I) with length 52 | 36−1, defining interval I = [0,33], and minimum distance d ≥ |{−1,0,…,33}|+1 = 36 (BCH-bound) [i]
- linear OA(320, 26, F3, 14) (dual of [26, 6, 15]-code), using contraction [i] based on linear OA(346, 52, F3, 29) (dual of [52, 6, 30]-code), using the expurgated narrow-sense BCH-code C(I) with length 52 | 36−1, defining interval I = [0,27], and minimum distance d ≥ |{−1,0,…,27}|+1 = 30 (BCH-bound) [i]
- linear OA(319, 26, F3, 13) (dual of [26, 7, 14]-code), using contraction [i] based on linear OA(345, 52, F3, 27) (dual of [52, 7, 28]-code), using the expurgated narrow-sense BCH-code C(I) with length 52 | 36−1, defining interval I = [0,25], and minimum distance d ≥ |{−1,0,…,25}|+1 = 28 (BCH-bound) [i]
- linear OA(31, 5, F3, 1) (dual of [5, 4, 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 OOA(325, 16, F3, 2, 16) (dual of [(16, 2), 7, 17]-NRT-code) | [i] | OOA Folding | |