Information on Result #700545

Linear OA(251, 71, F2, 21) (dual of [71, 20, 22]-code), using construction XX applied to C1 = C({0,3,5,7,11,13,15,23,27}), C2 = C({0,3,5,7,9,11,13,15,23}), C3 = C1 + C2 = C({0,3,5,7,11,13,15,23}), and C∩ = C1 ∩ C2 = C({0,3,5,7,9,11,13,15,23,27}) based on
  1. linear OA(246, 63, F2, 19) (dual of [63, 17, 20]-code), using the primitive cyclic code C(A) with length 63 = 26−1, defining set A = {0,3,5,7,11,13,15,23,27}, and minimum distance d ≥ |{23,28,33,…,−13}|+1 = 20 (BCH-bound) [i]
  2. linear OA(246, 63, F2, 19) (dual of [63, 17, 20]-code), using the primitive cyclic code C(A) with length 63 = 26−1, defining set A = {0,3,5,7,9,11,13,15,23}, and minimum distance d ≥ |{13,18,23,…,−23}|+1 = 20 (BCH-bound) [i]
  3. linear OA(249, 63, F2, 21) (dual of [63, 14, 22]-code), using the primitive cyclic code C(A) with length 63 = 26−1, defining set A = {0,3,5,7,9,11,13,15,23,27}, and minimum distance d ≥ |{13,18,23,…,−13}|+1 = 22 (BCH-bound) [i]
  4. linear OA(243, 63, F2, 17) (dual of [63, 20, 18]-code), using the primitive cyclic code C(A) with length 63 = 26−1, defining set A = {0,3,5,7,11,13,15,23}, and minimum distance d ≥ |{23,28,33,…,−23}|+1 = 18 (BCH-bound) [i]
  5. linear OA(21, 4, F2, 1) (dual of [4, 3, 2]-code), using
  6. linear OA(21, 4, F2, 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(251, 71, F2, 20) (dual of [71, 20, 21]-code) [i]Strength Reduction
2Linear OA(250, 70, F2, 20) (dual of [70, 20, 21]-code) [i]Truncation
3Linear OA(248, 68, F2, 18) (dual of [68, 20, 19]-code) [i]