Information on Result #701246

Linear OA(538, 69, F5, 19) (dual of [69, 31, 20]-code), using construction XX applied to C1 = C({0,1,2,3,4,6,7,8,9,11,12,37}), C2 = C([0,16]), C3 = C1 + C2 = C([0,12]), and C∩ = C1 ∩ C2 = C({0,1,2,3,4,6,7,8,9,11,12,16,37}) based on
  1. linear OA(534, 62, F5, 18) (dual of [62, 28, 19]-code), using the cyclic code C(A) with length 62 | 53−1, defining set A = {0,1,2,3,4,6,7,8,9,11,12,37}, and minimum distance d ≥ |{−2,−1,…,15}|+1 = 19 (BCH-bound) [i]
  2. linear OA(534, 62, F5, 17) (dual of [62, 28, 18]-code), using the expurgated narrow-sense BCH-code C(I) with length 62 | 53−1, defining interval I = [0,16], and designed minimum distance d ≥ |I|+1 = 18 [i]
  3. linear OA(537, 62, F5, 19) (dual of [62, 25, 20]-code), using the cyclic code C(A) with length 62 | 53−1, defining set A = {0,1,2,3,4,6,7,8,9,11,12,16,37}, and minimum distance d ≥ |{−2,−1,…,16}|+1 = 20 (BCH-bound) [i]
  4. linear OA(531, 62, F5, 16) (dual of [62, 31, 17]-code), using the expurgated narrow-sense BCH-code C(I) with length 62 | 53−1, defining interval I = [0,12], and designed minimum distance d ≥ |I|+1 = 17 [i]
  5. linear OA(51, 4, F5, 1) (dual of [4, 3, 2]-code), using
  6. linear OA(50, 3, F5, 0) (dual of [3, 3, 1]-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 OA(539, 72, F5, 19) (dual of [72, 33, 20]-code) [i]VarÅ¡amov–Edel Lengthening
2Linear OOA(538, 34, F5, 2, 19) (dual of [(34, 2), 30, 20]-NRT-code) [i]OOA Folding