Information on Result #700955

Linear OA(3128, 141, F3, 72) (dual of [141, 13, 73]-code), using construction XX applied to C1 = C({0,1,2,4,5,7,8,10,11,13,16,17,19,20,22,25,26,31,34,35,38,40,67}), C2 = C([0,61]), C3 = C1 + C2 = C([0,40]), and C∩ = C1 ∩ C2 = C([0,67]) based on
  1. linear OA(3111, 121, F3, 65) (dual of [121, 10, 66]-code), using the cyclic code C(A) with length 121 | 35−1, defining set A = {0,1,2,4,5,7,8,10,11,13,16,17,19,20,22,25,26,31,34,35,38,40,67}, and minimum distance d ≥ |{−4,−3,…,60}|+1 = 66 (BCH-bound) [i]
  2. linear OA(3111, 121, F3, 68) (dual of [121, 10, 69]-code), using the expurgated narrow-sense BCH-code C(I) with length 121 | 35−1, defining interval I = [0,66], and minimum distance d ≥ |{−1,0,…,66}|+1 = 69 (BCH-bound) [i]
  3. linear OA(3116, 121, F3, 80) (dual of [121, 5, 81]-code), using the expurgated narrow-sense BCH-code C(I) with length 121 | 35−1, defining interval I = [0,75], and minimum distance d ≥ |{5,15,25,…,−52}|+1 = 81 (BCH-bound) [i]
  4. linear OA(3106, 121, F3, 62) (dual of [121, 15, 63]-code), using the expurgated narrow-sense BCH-code C(I) with length 121 | 35−1, defining interval I = [0,60], and minimum distance d ≥ |{−1,0,…,60}|+1 = 63 (BCH-bound) [i]
  5. linear OA(34, 9, F3, 3) (dual of [9, 5, 4]-code or 9-cap in PG(3,3)), using
  6. linear OA(38, 11, F3, 6) (dual of [11, 3, 7]-code), using
    • 2 times truncation [i] based on linear OA(310, 13, F3, 8) (dual of [13, 3, 9]-code), using
      • Simplex code S(3,3) [i]
      • the expurgated narrow-sense BCH-code C(I) with length 13 | 33−1, defining interval I = [0,6], and minimum distance d ≥ |{−1,0,…,6}|+1 = 9 (BCH-bound) [i]

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(3128, 70, F3, 2, 72) (dual of [(70, 2), 12, 73]-NRT-code) [i]OOA Folding
2Linear OOA(3128, 47, F3, 3, 72) (dual of [(47, 3), 13, 73]-NRT-code) [i]
3Linear OOA(3128, 28, F3, 5, 72) (dual of [(28, 5), 12, 73]-NRT-code) [i]