Information on Result #737414

Linear OA(4181, 1093, F4, 42) (dual of [1093, 912, 43]-code), using construction X applied to Ce(41) ⊂ Ce(29) based on
  1. linear OA(4156, 1024, F4, 42) (dual of [1024, 868, 43]-code), using an extension Ce(41) of the primitive narrow-sense BCH-code C(I) with length 1023 = 45−1, defining interval I = [1,41], and designed minimum distance d ≥ |I|+1 = 42 [i]
  2. linear OA(4111, 1024, F4, 30) (dual of [1024, 913, 31]-code), using an extension Ce(29) of the primitive narrow-sense BCH-code C(I) with length 1023 = 45−1, defining interval I = [1,29], and designed minimum distance d ≥ |I|+1 = 30 [i]
  3. linear OA(425, 69, F4, 11) (dual of [69, 44, 12]-code), using
    • construction XX applied to C1 = C({0,1,2,3,5,6,7,47}), C2 = C([0,9]), C3 = C1 + C2 = C([0,7]), and C∩ = C1 ∩ C2 = C({0,1,2,3,5,6,7,9,47}) [i] based on
      1. 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]
      2. linear OA(422, 63, F4, 10) (dual of [63, 41, 11]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 63 = 43−1, defining interval I = [0,9], and designed minimum distance d ≥ |I|+1 = 11 [i]
      3. linear OA(425, 63, F4, 11) (dual of [63, 38, 12]-code), using the primitive cyclic code C(A) with length 63 = 43−1, defining set A = {0,1,2,3,5,6,7,9,47}, and minimum distance d ≥ |{−1,0,…,9}|+1 = 12 (BCH-bound) [i]
      4. linear OA(419, 63, F4, 9) (dual of [63, 44, 10]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 63 = 43−1, defining interval I = [0,7], and designed minimum distance d ≥ |I|+1 = 10 [i]
      5. linear OA(40, 3, F4, 0) (dual of [3, 3, 1]-code), using
      6. linear OA(40, 3, F4, 0) (dual of [3, 3, 1]-code) (see above)

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.