Information on Result #677823
Linear OA(324, 31, F3, 16) (dual of [31, 7, 17]-code), using construction XX applied to C1 = C([0,27]), C2 = C([1,33]), C3 = C1 + C2 = C([1,27]), and C∩ = C1 ∩ C2 = C([0,33]) based on
- 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(322, 26, F3, 16) (dual of [26, 4, 17]-code), using contraction [i] based on linear OA(348, 52, F3, 33) (dual of [52, 4, 34]-code), using the narrow-sense BCH-code C(I) with length 52 | 36−1, defining interval I = [1,33], and designed minimum distance d ≥ |I|+1 = 34 [i]
- 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(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 narrow-sense BCH-code C(I) with length 52 | 36−1, defining interval I = [1,27], and designed minimum distance d ≥ |I|+1 = 28 [i]
- linear OA(30, 1, F3, 0) (dual of [1, 1, 1]-code), using
- dual of repetition code with length 1 [i]
- linear OA(31, 4, F3, 1) (dual of [4, 3, 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(3192, 199, F3, 124) (dual of [199, 7, 125]-code) | [i] | Juxtaposition | |
| 2 | Linear OA(3136, 143, F3, 88) (dual of [143, 7, 89]-code) | [i] | ||
| 3 | Linear OA(3230, 269, F3, 109) (dual of [269, 39, 110]-code) | [i] | Construction X with Varšamov Bound | |
| 4 | Linear OA(3232, 271, F3, 110) (dual of [271, 39, 111]-code) | [i] | ||