Information on Result #701263

Linear OA(545, 77, F5, 21) (dual of [77, 32, 22]-code), using construction XX applied to C1 = C({0,1,2,3,4,6,7,8,9,11,12,37}), C2 = C([1,17]), C3 = C1 + C2 = C([1,12]), and C∩ = C1 ∩ C2 = C({0,1,2,3,4,6,7,8,9,11,12,16,17,37}) 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(536, 62, F5, 18) (dual of [62, 26, 19]-code), using the narrow-sense BCH-code C(I) with length 62 | 53−1, defining interval I = [1,17], and designed minimum distance d ≥ |I|+1 = 19 [i]
  3. 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]
  4. linear OA(530, 62, F5, 15) (dual of [62, 32, 16]-code), using the narrow-sense BCH-code C(I) with length 62 | 53−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 16 [i]
  5. linear OA(52, 6, F5, 2) (dual of [6, 4, 3]-code or 6-arc in PG(1,5)), using
  6. linear OA(53, 9, F5, 2) (dual of [9, 6, 3]-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(545, 77, F5, 20) (dual of [77, 32, 21]-code) [i]Strength Reduction
2Linear OOA(545, 38, F5, 2, 21) (dual of [(38, 2), 31, 22]-NRT-code) [i]OOA Folding