Information on Result #731741

Linear OA(3130, 137, F3, 82) (dual of [137, 7, 83]-code), using juxtaposition based on
  1. linear OA(319, 26, F3, 13) (dual of [26, 7, 14]-code), using
    • contraction [i] based on linear OA(345, 52, F3, 27) (dual of [52, 7, 28]-code), using the expurgated narrow-sense BCH-code C(I) with length 52 | 36−1, defining interval I = [0,25], and minimum distance d ≥ |{−1,0,…,25}|+1 = 28 (BCH-bound) [i]
  2. linear OA(3104, 111, F3, 68) (dual of [111, 7, 69]-code), using
    • construction XX applied to Ce(79) ⊂ Ce(52) ⊂ Ce(49) [i] based on
      1. linear OA(380, 81, F3, 80) (dual of [81, 1, 81]-code or 81-arc in PG(79,3)), using an extension Ce(79) of the primitive narrow-sense BCH-code C(I) with length 80 = 34−1, defining interval I = [1,79], and designed minimum distance d ≥ |I|+1 = 80 [i]
      2. linear OA(376, 81, F3, 53) (dual of [81, 5, 54]-code), using an extension Ce(52) of the primitive narrow-sense BCH-code C(I) with length 80 = 34−1, defining interval I = [1,52], and designed minimum distance d ≥ |I|+1 = 53 [i]
      3. linear OA(374, 81, F3, 50) (dual of [81, 7, 51]-code), using an extension Ce(49) of the primitive narrow-sense BCH-code C(I) with length 80 = 34−1, defining interval I = [1,49], and designed minimum distance d ≥ |I|+1 = 50 [i]
      4. linear OA(320, 26, F3, 14) (dual of [26, 6, 15]-code), using
        • contraction [i] based on linear OA(346, 52, F3, 29) (dual of [52, 6, 30]-code), using the expurgated narrow-sense BCH-code C(I) with length 52 | 36−1, defining interval I = [0,27], and minimum distance d ≥ |{−1,0,…,27}|+1 = 30 (BCH-bound) [i]
      5. linear OA(32, 4, F3, 2) (dual of [4, 2, 3]-code or 4-arc in PG(1,3)), 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.

Compare with Markus Grassl’s online database of code parameters.

Other Results with Identical Parameters

None.

Depending Results

None.