Information on Result #700956

Linear OA(3144, 155, F3, 84) (dual of [155, 11, 85]-code), using construction XX applied to C1 = C({1,2,4,5,7,8,10,11,13,16,17,19,20,22,25,26,31,34,35,38,40,61,76}), C2 = C([1,67]), C3 = C1 + C2 = C([1,61]), and C∩ = C1 ∩ C2 = C([1,76]) based on
  1. linear OA(3115, 121, F3, 75) (dual of [121, 6, 76]-code), using the cyclic code C(A) with length 121 | 35−1, defining set A = {1,2,4,5,7,8,10,11,13,16,17,19,20,22,25,26,31,34,35,38,40,61,76}, and minimum distance d ≥ |{10,26,42,…,−16}|+1 = 76 (BCH-bound) [i]
  2. linear OA(3115, 121, F3, 75) (dual of [121, 6, 76]-code), using the narrow-sense BCH-code C(I) with length 121 | 35−1, defining interval I = [1,75], and designed minimum distance d ≥ |I|+1 = 76 [i]
  3. linear OA(3120, 121, F3, 120) (dual of [121, 1, 121]-code or 121-arc in PG(119,3)), using the narrow-sense BCH-code C(I) with length 121 | 35−1, defining interval I = [1,76], and designed minimum distance d ≥ |I|+1 = 121 [i]
  4. linear OA(3110, 121, F3, 66) (dual of [121, 11, 67]-code), using the narrow-sense BCH-code C(I) with length 121 | 35−1, defining interval I = [1,66], and designed minimum distance d ≥ |I|+1 = 67 [i]
  5. linear OA(312, 17, F3, 8) (dual of [17, 5, 9]-code), using
  6. linear OA(312, 17, F3, 8) (dual of [17, 5, 9]-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(3144, 31, F3, 5, 84) (dual of [(31, 5), 11, 85]-NRT-code) [i]OOA Folding