Information on Result #731752

Linear OA(3199, 206, F3, 128) (dual of [206, 7, 129]-code), using juxtaposition based on
  1. 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]
  2. linear OA(3118, 125, F3, 77) (dual of [125, 7, 78]-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(334, 40, F3, 23) (dual of [40, 6, 24]-code), using
        • the expurgated narrow-sense BCH-code C(I) with length 40 | 34−1, defining interval I = [0,21], and minimum distance d ≥ |{−1,0,…,21}|+1 = 24 (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.