Information on Result #1299920

Linear OA(478, 1056, F4, 19) (dual of [1056, 978, 20]-code), using construction X with VarÅ¡amov bound based on
  1. linear OA(477, 1054, F4, 19) (dual of [1054, 977, 20]-code), using
    • construction XX applied to C1 = C([1019,12]), C2 = C([0,14]), C3 = C1 + C2 = C([0,12]), and C∩ = C1 ∩ C2 = C([1019,14]) [i] based on
      1. linear OA(461, 1023, F4, 17) (dual of [1023, 962, 18]-code), using the primitive BCH-code C(I) with length 1023 = 45−1, defining interval I = {−4,−3,…,12}, and designed minimum distance d ≥ |I|+1 = 18 [i]
      2. linear OA(456, 1023, F4, 15) (dual of [1023, 967, 16]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 1023 = 45−1, defining interval I = [0,14], and designed minimum distance d ≥ |I|+1 = 16 [i]
      3. linear OA(471, 1023, F4, 19) (dual of [1023, 952, 20]-code), using the primitive BCH-code C(I) with length 1023 = 45−1, defining interval I = {−4,−3,…,14}, and designed minimum distance d ≥ |I|+1 = 20 [i]
      4. linear OA(446, 1023, F4, 13) (dual of [1023, 977, 14]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 1023 = 45−1, defining interval I = [0,12], and designed minimum distance d ≥ |I|+1 = 14 [i]
      5. linear OA(45, 20, F4, 3) (dual of [20, 15, 4]-code or 20-cap in PG(4,4)), using
      6. linear OA(41, 11, F4, 1) (dual of [11, 10, 2]-code), using
  2. linear OA(477, 1055, F4, 18) (dual of [1055, 978, 19]-code), using Gilbert–VarÅ¡amov bound and bm = 477 > Vbs−1(k−1) = 784 019920 201681 676254 284824 451017 247769 959721 [i]
  3. linear OA(40, 1, F4, 0) (dual of [1, 1, 1]-code), 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.

Other Results with Identical Parameters

None.

Depending Results

None.