Information on Result #737301

Linear OA(4205, 4169, F4, 40) (dual of [4169, 3964, 41]-code), using construction X applied to C([0,20]) ⊂ C([0,14]) based on
  1. linear OA(4181, 4097, F4, 41) (dual of [4097, 3916, 42]-code), using the expurgated narrow-sense BCH-code C(I) with length 4097 | 412−1, defining interval I = [0,20], and minimum distance d ≥ |{−20,−19,…,20}|+1 = 42 (BCH-bound) [i]
  2. linear OA(4133, 4097, F4, 29) (dual of [4097, 3964, 30]-code), using the expurgated narrow-sense BCH-code C(I) with length 4097 | 412−1, defining interval I = [0,14], and minimum distance d ≥ |{−14,−13,…,14}|+1 = 30 (BCH-bound) [i]
  3. linear OA(424, 72, F4, 10) (dual of [72, 48, 11]-code), using
    • construction XX applied to C1 = C({0,1,2,3,5,6,47}), C2 = C([1,7]), C3 = C1 + C2 = C([1,6]), and C∩ = C1 ∩ C2 = C({0,1,2,3,5,6,7,47}) [i] based on
      1. linear OA(419, 63, F4, 8) (dual of [63, 44, 9]-code), using the primitive cyclic code C(A) with length 63 = 43−1, defining set A = {0,1,2,3,5,6,47}, and minimum distance d ≥ |{−1,0,…,6}|+1 = 9 (BCH-bound) [i]
      2. linear OA(418, 63, F4, 8) (dual of [63, 45, 9]-code), using the primitive narrow-sense BCH-code C(I) with length 63 = 43−1, defining interval I = [1,7], and designed minimum distance d ≥ |I|+1 = 9 [i]
      3. linear OA(422, 63, F4, 10) (dual of [63, 41, 11]-code), using the primitive cyclic code C(A) with length 63 = 43−1, defining set A = {0,1,2,3,5,6,7,47}, and minimum distance d ≥ |{−1,0,…,8}|+1 = 11 (BCH-bound) [i]
      4. linear OA(415, 63, F4, 6) (dual of [63, 48, 7]-code), using the primitive narrow-sense BCH-code C(I) with length 63 = 43−1, defining interval I = [1,6], and designed minimum distance d ≥ |I|+1 = 7 [i]
      5. linear OA(41, 5, F4, 1) (dual of [5, 4, 2]-code), using
      6. linear OA(41, 4, F4, 1) (dual of [4, 3, 2]-code), 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.

Other Results with Identical Parameters

None.

Depending Results

None.