Information on Result #705780

Linear OA(3248, 777, F3, 61) (dual of [777, 529, 62]-code), using construction XX applied to C1 = C([307,363]), C2 = C([315,367]), C3 = C1 + C2 = C([315,363]), and C∩ = C1 ∩ C2 = C([307,367]) based on
  1. linear OA(3216, 728, F3, 57) (dual of [728, 512, 58]-code), using the primitive BCH-code C(I) with length 728 = 36−1, defining interval I = {307,308,…,363}, and designed minimum distance d ≥ |I|+1 = 58 [i]
  2. linear OA(3208, 728, F3, 53) (dual of [728, 520, 54]-code), using the primitive BCH-code C(I) with length 728 = 36−1, defining interval I = {315,316,…,367}, and designed minimum distance d ≥ |I|+1 = 54 [i]
  3. linear OA(3229, 728, F3, 61) (dual of [728, 499, 62]-code), using the primitive BCH-code C(I) with length 728 = 36−1, defining interval I = {307,308,…,367}, and designed minimum distance d ≥ |I|+1 = 62 [i]
  4. linear OA(3195, 728, F3, 49) (dual of [728, 533, 50]-code), using the primitive BCH-code C(I) with length 728 = 36−1, defining interval I = {315,316,…,363}, and designed minimum distance d ≥ |I|+1 = 50 [i]
  5. linear OA(314, 31, F3, 7) (dual of [31, 17, 8]-code), using
    • construction X applied to Ce(6) ⊂ Ce(4) [i] based on
      1. linear OA(313, 27, F3, 7) (dual of [27, 14, 8]-code), using an extension Ce(6) of the primitive narrow-sense BCH-code C(I) with length 26 = 33−1, defining interval I = [1,6], and designed minimum distance d ≥ |I|+1 = 7 [i]
      2. linear OA(310, 27, F3, 5) (dual of [27, 17, 6]-code), using an extension Ce(4) of the primitive narrow-sense BCH-code C(I) with length 26 = 33−1, defining interval I = [1,4], and designed minimum distance d ≥ |I|+1 = 5 [i]
      3. linear OA(31, 4, F3, 1) (dual of [4, 3, 2]-code), using
  6. linear OA(35, 18, F3, 3) (dual of [18, 13, 4]-code or 18-cap in PG(4,3)), 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.