Information on Result #705569

Linear OA(3234, 785, F3, 55) (dual of [785, 551, 56]-code), using construction XX applied to C1 = C([722,43]), C2 = C([1,48]), C3 = C1 + C2 = C([1,43]), and C∩ = C1 ∩ C2 = C([722,48]) based on
  1. linear OA(3196, 728, F3, 50) (dual of [728, 532, 51]-code), using the primitive BCH-code C(I) with length 728 = 36−1, defining interval I = {−6,−5,…,43}, and designed minimum distance d ≥ |I|+1 = 51 [i]
  2. linear OA(3189, 728, F3, 48) (dual of [728, 539, 49]-code), using the primitive narrow-sense BCH-code C(I) with length 728 = 36−1, defining interval I = [1,48], and designed minimum distance d ≥ |I|+1 = 49 [i]
  3. linear OA(3214, 728, F3, 55) (dual of [728, 514, 56]-code), using the primitive BCH-code C(I) with length 728 = 36−1, defining interval I = {−6,−5,…,48}, and designed minimum distance d ≥ |I|+1 = 56 [i]
  4. linear OA(3171, 728, F3, 43) (dual of [728, 557, 44]-code), using the primitive narrow-sense BCH-code C(I) with length 728 = 36−1, defining interval I = [1,43], and designed minimum distance d ≥ |I|+1 = 44 [i]
  5. linear OA(313, 32, F3, 6) (dual of [32, 19, 7]-code), using
    • construction XX applied to C1 = C({0,1,2,17}), C2 = C([0,4]), C3 = C1 + C2 = C([0,2]), and C∩ = C1 ∩ C2 = C({0,1,2,4,17}) [i] based on
      1. linear OA(310, 26, F3, 5) (dual of [26, 16, 6]-code), using the primitive cyclic code C(A) with length 26 = 33−1, defining set A = {0,1,2,17}, and minimum distance d ≥ |{−1,0,1,2,3}|+1 = 6 (BCH-bound) [i]
      2. linear OA(310, 26, F3, 5) (dual of [26, 16, 6]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 26 = 33−1, defining interval I = [0,4], and designed minimum distance d ≥ |I|+1 = 6 [i]
      3. linear OA(313, 26, F3, 6) (dual of [26, 13, 7]-code), using the primitive cyclic code C(A) with length 26 = 33−1, defining set A = {0,1,2,4,17}, and minimum distance d ≥ |{−1,0,…,4}|+1 = 7 (BCH-bound) [i]
      4. linear OA(37, 26, F3, 4) (dual of [26, 19, 5]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 26 = 33−1, defining interval I = [0,2], and designed minimum distance d ≥ |I|+1 = 5 [i]
      5. linear OA(30, 3, F3, 0) (dual of [3, 3, 1]-code), using
      6. linear OA(30, 3, F3, 0) (dual of [3, 3, 1]-code) (see above)
  6. linear OA(37, 25, F3, 4) (dual of [25, 18, 5]-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.

Other Results with Identical Parameters

None.

Depending Results

None.