Information on Result #1298120

Linear OA(383, 100, F3, 44) (dual of [100, 17, 45]-code), using construction X with VarÅ¡amov bound based on
  1. linear OA(374, 90, F3, 44) (dual of [90, 16, 45]-code), using
    • construction XX applied to C1 = C([0,79]), C2 = C([1,87]), C3 = C1 + C2 = C([1,79]), and C∩ = C1 ∩ C2 = C([0,87]) [i] based on
      1. linear OA(365, 80, F3, 40) (dual of [80, 15, 41]-code), using contraction [i] based on linear OA(3145, 160, F3, 81) (dual of [160, 15, 82]-code), using the expurgated narrow-sense BCH-code C(I) with length 160 | 38−1, defining interval I = [0,79], and minimum distance d ≥ |{−1,0,…,79}|+1 = 82 (BCH-bound) [i]
      2. linear OA(369, 80, F3, 43) (dual of [80, 11, 44]-code), using contraction [i] based on linear OA(3149, 160, F3, 87) (dual of [160, 11, 88]-code), using the narrow-sense BCH-code C(I) with length 160 | 38−1, defining interval I = [1,87], and designed minimum distance d ≥ |I|+1 = 88 [i]
      3. linear OA(370, 80, F3, 44) (dual of [80, 10, 45]-code), using contraction [i] based on linear OA(3150, 160, F3, 89) (dual of [160, 10, 90]-code), using the expurgated narrow-sense BCH-code C(I) with length 160 | 38−1, defining interval I = [0,87], and minimum distance d ≥ |{−1,0,…,87}|+1 = 90 (BCH-bound) [i]
      4. linear OA(364, 80, F3, 39) (dual of [80, 16, 40]-code), using contraction [i] based on linear OA(3144, 160, F3, 79) (dual of [160, 16, 80]-code), using the narrow-sense BCH-code C(I) with length 160 | 38−1, defining interval I = [1,79], and designed minimum distance d ≥ |I|+1 = 80 [i]
      5. linear OA(30, 1, F3, 0) (dual of [1, 1, 1]-code), using
      6. linear OA(34, 9, F3, 3) (dual of [9, 5, 4]-code or 9-cap in PG(3,3)), using
  2. linear OA(374, 91, F3, 35) (dual of [91, 17, 36]-code), using Gilbert–VarÅ¡amov bound and bm = 374 > Vbs−1(k−1) = 171931 097596 428852 789045 106300 650729 [i]
  3. linear OA(38, 9, F3, 8) (dual of [9, 1, 9]-code or 9-arc in PG(7,3)), using

Mode: 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.