Information on Result #677623

Linear OA(381, 92, F3, 50) (dual of [92, 11, 51]-code), using construction XX applied to C([0,99]) ⊂ C([0,87]) ⊂ C([1,87]) based on
  1. linear OA(374, 80, F3, 50) (dual of [80, 6, 51]-code), using contraction [i] based on linear OA(3154, 160, F3, 101) (dual of [160, 6, 102]-code), using the expurgated narrow-sense BCH-code C(I) with length 160 | 38−1, defining interval I = [0,99], and minimum distance d ≥ |{−1,0,…,99}|+1 = 102 (BCH-bound) [i]
  2. linear OA(370, 80, F3, 44) (dual of [80, 10, 45]-code), using contraction [i] based on linear OA(3150, 160, F3, 89) (dual of [160, 10, 90]-code), using the expurgated narrow-sense BCH-code C(I) with length 160 | 38−1, defining interval I = [0,87], and minimum distance d ≥ |{−1,0,…,87}|+1 = 90 (BCH-bound) [i]
  3. 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]
  4. linear OA(36, 11, F3, 5) (dual of [11, 5, 6]-code), using
  5. linear OA(30, 1, F3, 0) (dual of [1, 1, 1]-code), 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:

ResultThis
result
only		Method
1Linear OA(381, 92, F3, 49) (dual of [92, 11, 50]-code) [i]Strength Reduction
2Linear OA(378, 89, F3, 47) (dual of [89, 11, 48]-code) [i]Truncation
3Linear OOA(381, 46, F3, 2, 50) (dual of [(46, 2), 11, 51]-NRT-code) [i]OOA Folding
4Linear OOA(381, 23, F3, 4, 50) (dual of [(23, 4), 11, 51]-NRT-code) [i]