Information on Result #1299822

Linear OA(456, 84, F4, 27) (dual of [84, 28, 28]-code), using construction X with VarÅ¡amov bound based on
  1. linear OA(451, 76, F4, 27) (dual of [76, 25, 28]-code), using
    • construction XX applied to C1 = C({0,1,2,3,5,6,7,9,10,11,13,14,15,21,31,47}), C2 = C([0,22]), C3 = C1 + C2 = C([0,21]), and C∩ = C1 ∩ C2 = C({0,1,2,3,5,6,7,9,10,11,13,14,15,21,22,31,47}) [i] based on
      1. linear OA(444, 63, F4, 26) (dual of [63, 19, 27]-code), using the primitive cyclic code C(A) with length 63 = 43−1, defining set A = {0,1,2,3,5,6,7,9,10,11,13,14,15,21,31,47}, and minimum distance d ≥ |{−4,−3,…,21}|+1 = 27 (BCH-bound) [i]
      2. linear OA(441, 63, F4, 23) (dual of [63, 22, 24]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 63 = 43−1, defining interval I = [0,22], and designed minimum distance d ≥ |I|+1 = 24 [i]
      3. linear OA(447, 63, F4, 27) (dual of [63, 16, 28]-code), using the primitive cyclic code C(A) with length 63 = 43−1, defining set A = {0,1,2,3,5,6,7,9,10,11,13,14,15,21,22,31,47}, and minimum distance d ≥ |{−4,−3,…,22}|+1 = 28 (BCH-bound) [i]
      4. linear OA(438, 63, F4, 22) (dual of [63, 25, 23]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 63 = 43−1, defining interval I = [0,21], and designed minimum distance d ≥ |I|+1 = 23 [i]
      5. linear OA(44, 10, F4, 3) (dual of [10, 6, 4]-code or 10-cap in PG(3,4)), using
      6. linear OA(40, 3, F4, 0) (dual of [3, 3, 1]-code), using
  2. linear OA(451, 79, F4, 24) (dual of [79, 28, 25]-code), using Gilbert–VarÅ¡amov bound and bm = 451 > Vbs−1(k−1) = 3 757723 337813 437223 138875 343824 [i]
  3. linear OA(42, 5, F4, 2) (dual of [5, 3, 3]-code or 5-arc in PG(1,4)), 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.