Information on Result #1299800

Linear OA(454, 83, F4, 26) (dual of [83, 29, 27]-code), using construction X with VarÅ¡amov bound based on
  1. linear OA(448, 74, F4, 26) (dual of [74, 26, 27]-code), using
    • construction XX applied to C1 = C([0,65]), C2 = C([1,77]), C3 = C1 + C2 = C([1,65]), and C∩ = C1 ∩ C2 = C([0,77]) [i] based on
      1. linear OA(438, 63, F4, 22) (dual of [63, 25, 23]-code), using contraction [i] based on linear OA(4164, 189, F4, 68) (dual of [189, 25, 69]-code), using the expurgated narrow-sense BCH-code C(I) with length 189 | 49−1, defining interval I = [0,65], and minimum distance d ≥ |{−2,−1,…,65}|+1 = 69 (BCH-bound) [i]
      2. linear OA(443, 63, F4, 25) (dual of [63, 20, 26]-code), using contraction [i] based on linear OA(4169, 189, F4, 77) (dual of [189, 20, 78]-code), using the narrow-sense BCH-code C(I) with length 189 | 49−1, defining interval I = [1,77], and designed minimum distance d ≥ |I|+1 = 78 [i]
      3. linear OA(444, 63, F4, 26) (dual of [63, 19, 27]-code), using contraction [i] based on linear OA(4170, 189, F4, 80) (dual of [189, 19, 81]-code), using the expurgated narrow-sense BCH-code C(I) with length 189 | 49−1, defining interval I = [0,77], and minimum distance d ≥ |{−2,−1,…,77}|+1 = 81 (BCH-bound) [i]
      4. linear OA(437, 63, F4, 21) (dual of [63, 26, 22]-code), using contraction [i] based on linear OA(4163, 189, F4, 65) (dual of [189, 26, 66]-code), using the narrow-sense BCH-code C(I) with length 189 | 49−1, defining interval I = [1,65], and designed minimum distance d ≥ |I|+1 = 66 [i]
      5. linear OA(40, 1, F4, 0) (dual of [1, 1, 1]-code), using
      6. linear OA(44, 10, F4, 3) (dual of [10, 6, 4]-code or 10-cap in PG(3,4)), using
  2. linear OA(448, 77, F4, 22) (dual of [77, 29, 23]-code), using Gilbert–VarÅ¡amov bound and bm = 448 > Vbs−1(k−1) = 34704 291132 307503 590267 609464 [i]
  3. linear OA(43, 6, F4, 3) (dual of [6, 3, 4]-code or 6-arc in PG(2,4) or 6-cap in PG(2,4)), 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.