Information on Result #700823

Linear OA(349, 84, F3, 21) (dual of [84, 35, 22]-code), using construction XX applied to C1 = C({0,4,5,7,8,13,14,17,22,25,41,44,50}), C2 = C({0,4,5,7,8,10,13,14,17,22,25,41,44}), C3 = C1 + C2 = C({0,4,5,7,8,13,14,17,22,25,41,44}), and C∩ = C1 ∩ C2 = C({0,4,5,7,8,10,13,14,17,22,25,41,44,50}) based on
  1. linear OA(347, 80, F3, 20) (dual of [80, 33, 21]-code), using the primitive cyclic code C(A) with length 80 = 34−1, defining set A = {0,4,5,7,8,13,14,17,22,25,41,44,50}, and minimum distance d ≥ |{17,24,31,…,−10}|+1 = 21 (BCH-bound) [i]
  2. linear OA(347, 80, F3, 20) (dual of [80, 33, 21]-code), using the primitive cyclic code C(A) with length 80 = 34−1, defining set A = {0,4,5,7,8,10,13,14,17,22,25,41,44}, and minimum distance d ≥ |{10,17,24,…,−17}|+1 = 21 (BCH-bound) [i]
  3. linear OA(349, 80, F3, 21) (dual of [80, 31, 22]-code), using the primitive cyclic code C(A) with length 80 = 34−1, defining set A = {0,4,5,7,8,10,13,14,17,22,25,41,44,50}, and minimum distance d ≥ |{10,17,24,…,−10}|+1 = 22 (BCH-bound) [i]
  4. linear OA(345, 80, F3, 19) (dual of [80, 35, 20]-code), using the primitive cyclic code C(A) with length 80 = 34−1, defining set A = {0,4,5,7,8,13,14,17,22,25,41,44}, and minimum distance d ≥ |{17,24,31,…,−17}|+1 = 20 (BCH-bound) [i]
  5. linear OA(30, 2, F3, 0) (dual of [2, 2, 1]-code), using
  6. linear OA(30, 2, F3, 0) (dual of [2, 2, 1]-code) (see above)

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(351, 86, F3, 21) (dual of [86, 35, 22]-code) [i]Code Embedding in Larger Space
2Linear OOA(349, 42, F3, 2, 21) (dual of [(42, 2), 35, 22]-NRT-code) [i]OOA Folding