Information on Result #700992

Linear OA(427, 74, F4, 11) (dual of [74, 47, 12]-code), using construction XX applied to C1 = C({0,1,2,3,5,6,31,47}), C2 = C([0,7]), C3 = C1 + C2 = C([0,6]), and C∩ = C1 ∩ C2 = C({0,1,2,3,5,6,7,31,47}) based on
  1. linear OA(422, 63, F4, 9) (dual of [63, 41, 10]-code), using the primitive cyclic code C(A) with length 63 = 43−1, defining set A = {0,1,2,3,5,6,31,47}, and minimum distance d ≥ |{−2,−1,…,6}|+1 = 10 (BCH-bound) [i]
  2. 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]
  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 = {0,1,2,3,5,6,7,31,47}, and minimum distance d ≥ |{−2,−1,…,8}|+1 = 12 (BCH-bound) [i]
  4. linear OA(416, 63, F4, 7) (dual of [63, 47, 8]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 63 = 43−1, defining interval I = [0,6], and designed minimum distance d ≥ |I|+1 = 8 [i]
  5. linear OA(41, 7, F4, 1) (dual of [7, 6, 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.

Compare with Markus Grassl’s online database of code parameters.

Other Results with Identical Parameters

None.

Depending Results

The following results depend on this result:

ResultThis
result
only		Method
1Linear OOA(427, 71, F4, 2, 11) (dual of [(71, 2), 115, 12]-NRT-code) [i]Embedding of OOA with Gilbert–VarÅ¡amov Bound
2Linear OOA(427, 71, F4, 3, 11) (dual of [(71, 3), 186, 12]-NRT-code) [i]
3Digital (16, 27, 71)-net over F4 [i]
4Linear OOA(427, 37, F4, 2, 11) (dual of [(37, 2), 47, 12]-NRT-code) [i]OOA Folding