Information on Result #700932

Linear OA(370, 131, F3, 24) (dual of [131, 61, 25]-code), using construction XX applied to C1 = C({1,4,7,8,10,13,16,19,22,25,26,31,34}), C2 = C({1,4,7,8,10,13,16,19,20,22,25,26,31}), C3 = C1 + C2 = C({1,4,7,8,10,13,16,19,22,25,26,31}), and C∩ = C1 ∩ C2 = C({1,4,7,8,10,13,16,19,20,22,25,26,31,34}) based on
  1. linear OA(365, 121, F3, 23) (dual of [121, 56, 24]-code), using the cyclic code C(A) with length 121 | 35−1, defining set A = {1,4,7,8,10,13,16,19,22,25,26,31,34}, and minimum distance d ≥ |{−50,−30,−10,…,27}|+1 = 24 (BCH-bound) [i]
  2. linear OA(365, 121, F3, 23) (dual of [121, 56, 24]-code), using the cyclic code C(A) with length 121 | 35−1, defining set A = {1,4,7,8,10,13,16,19,20,22,25,26,31}, and minimum distance d ≥ |{−30,−10,10,…,47}|+1 = 24 (BCH-bound) [i]
  3. linear OA(370, 121, F3, 24) (dual of [121, 51, 25]-code), using the cyclic code C(A) with length 121 | 35−1, defining set A = {1,4,7,8,10,13,16,19,20,22,25,26,31,34}, and minimum distance d ≥ |{−50,−30,−10,…,47}|+1 = 25 (BCH-bound) [i]
  4. linear OA(360, 121, F3, 22) (dual of [121, 61, 23]-code), using the cyclic code C(A) with length 121 | 35−1, defining set A = {1,4,7,8,10,13,16,19,22,25,26,31}, and minimum distance d ≥ |{−30,−10,10,…,27}|+1 = 23 (BCH-bound) [i]
  5. linear OA(30, 5, F3, 0) (dual of [5, 5, 1]-code), using
  6. linear OA(30, 5, F3, 0) (dual of [5, 5, 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 OOA(370, 65, F3, 2, 24) (dual of [(65, 2), 60, 25]-NRT-code) [i]OOA Folding
2Linear OOA(370, 43, F3, 3, 24) (dual of [(43, 3), 59, 25]-NRT-code) [i]