Information on Result #700810

Linear OA(391, 106, F3, 51) (dual of [106, 15, 52]-code), using construction XX applied to C1 = C({0,1,2,4,5,7,8,10,11,13,14,16,17,20,22,23,25,26,40,44,53}), C2 = C([1,41]), C3 = C1 + C2 = C([1,40]), and C∩ = C1 ∩ C2 = C({0,1,2,4,5,7,8,10,11,13,14,16,17,20,22,23,25,26,40,41,44,53}) based on
  1. linear OA(374, 80, F3, 50) (dual of [80, 6, 51]-code), using the primitive cyclic code C(A) with length 80 = 34−1, defining set A = {0,1,2,4,5,7,8,10,11,13,14,16,17,20,22,23,25,26,40,44,53}, and minimum distance d ≥ |{−9,−8,…,40}|+1 = 51 (BCH-bound) [i]
  2. linear OA(369, 80, F3, 43) (dual of [80, 11, 44]-code), using the primitive narrow-sense BCH-code C(I) with length 80 = 34−1, defining interval I = [1,41], and designed minimum distance d ≥ |I|+1 = 44 [i]
  3. linear OA(378, 80, F3, 59) (dual of [80, 2, 60]-code), using the primitive cyclic code C(A) with length 80 = 34−1, defining set A = {0,1,2,4,5,7,8,10,11,13,14,16,17,20,22,23,25,26,40,41,44,53}, and minimum distance d ≥ |{3,16,29,…,37}|+1 = 60 (BCH-bound) [i]
  4. linear OA(365, 80, F3, 40) (dual of [80, 15, 41]-code), using the primitive narrow-sense BCH-code C(I) with length 80 = 34−1, defining interval I = [1,40], and designed minimum distance d ≥ |I|+1 = 41 [i]
  5. linear OA(312, 21, F3, 8) (dual of [21, 9, 9]-code), using
  6. linear OA(31, 5, F3, 1) (dual of [5, 4, 2]-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 OOA(391, 53, F3, 2, 51) (dual of [(53, 2), 15, 52]-NRT-code) [i]OOA Folding