Information on Result #700549

Linear OA(275, 91, F2, 32) (dual of [91, 16, 33]-code), using construction XX applied to C1 = C({1,3,5,7,9,11,13,15,21,27,31}), C2 = C([1,23]), C3 = C1 + C2 = C([1,21]), and C∩ = C1 ∩ C2 = C([1,31]) based on
  1. linear OA(256, 63, F2, 30) (dual of [63, 7, 31]-code), using the primitive cyclic code C(A) with length 63 = 26−1, defining set A = {1,3,5,7,9,11,13,15,21,27,31}, and minimum distance d ≥ |{5,10,15,…,24}|+1 = 31 (BCH-bound) [i]
  2. linear OA(253, 63, F2, 26) (dual of [63, 10, 27]-code), using the primitive narrow-sense BCH-code C(I) with length 63 = 26−1, defining interval I = [1,23], and designed minimum distance d ≥ |I|+1 = 27 [i]
  3. linear OA(262, 63, F2, 62) (dual of [63, 1, 63]-code or 63-arc in PG(61,2)), using the primitive narrow-sense BCH-code C(I) with length 63 = 26−1, defining interval I = [1,31], and designed minimum distance d ≥ |I|+1 = 63 [i]
  4. linear OA(247, 63, F2, 22) (dual of [63, 16, 23]-code), using the primitive narrow-sense BCH-code C(I) with length 63 = 26−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 23 [i]
  5. linear OA(212, 21, F2, 7) (dual of [21, 9, 8]-code), using
  6. linear OA(21, 7, F2, 1) (dual of [7, 6, 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 OA(276, 92, F2, 33) (dual of [92, 16, 34]-code) [i]Adding a Parity Check Bit
2Linear OOA(275, 45, F2, 2, 32) (dual of [(45, 2), 15, 33]-NRT-code) [i]OOA Folding
3Linear OOA(275, 30, F2, 3, 32) (dual of [(30, 3), 15, 33]-NRT-code) [i]