Information on Result #701279

Linear OA(545, 70, F5, 23) (dual of [70, 25, 24]-code), using construction XX applied to C1 = C({0,1,2,3,4,6,7,8,9,11,12,16,17,37}), C2 = C([0,19]), C3 = C1 + C2 = C([0,17]), and C∩ = C1 ∩ C2 = C({0,1,2,3,4,6,7,8,9,11,12,16,17,19,37}) based on
  1. linear OA(540, 62, F5, 21) (dual of [62, 22, 22]-code), using the cyclic code C(A) with length 62 | 53−1, defining set A = {0,1,2,3,4,6,7,8,9,11,12,16,17,37}, and minimum distance d ≥ |{−2,−1,…,18}|+1 = 22 (BCH-bound) [i]
  2. linear OA(540, 62, F5, 21) (dual of [62, 22, 22]-code), using the expurgated narrow-sense BCH-code C(I) with length 62 | 53−1, defining interval I = [0,19], and designed minimum distance d ≥ |I|+1 = 22 [i]
  3. linear OA(543, 62, F5, 23) (dual of [62, 19, 24]-code), using the cyclic code C(A) with length 62 | 53−1, defining set A = {0,1,2,3,4,6,7,8,9,11,12,16,17,19,37}, and minimum distance d ≥ |{−2,−1,…,20}|+1 = 24 (BCH-bound) [i]
  4. linear OA(537, 62, F5, 19) (dual of [62, 25, 20]-code), using the expurgated narrow-sense BCH-code C(I) with length 62 | 53−1, defining interval I = [0,17], and designed minimum distance d ≥ |I|+1 = 20 [i]
  5. linear OA(51, 4, F5, 1) (dual of [4, 3, 2]-code), using
  6. linear OA(51, 4, F5, 1) (dual of [4, 3, 2]-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.

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(544, 69, F5, 22) (dual of [69, 25, 23]-code) [i]Truncation
2Linear OOA(545, 35, F5, 2, 23) (dual of [(35, 2), 25, 24]-NRT-code) [i]OOA Folding