Information on Result #700595

Linear OA(275, 158, F2, 20) (dual of [158, 83, 21]-code), using construction XX applied to C1 = C({0,1,3,5,7,9,11,63}), C2 = C([1,15]), C3 = C1 + C2 = C([1,11]), and C∩ = C1 ∩ C2 = C({0,1,3,5,7,9,11,13,15,63}) based on
  1. linear OA(250, 127, F2, 15) (dual of [127, 77, 16]-code), using the primitive cyclic code C(A) with length 127 = 27−1, defining set A = {0,1,3,5,7,9,11,63}, and minimum distance d ≥ |{−2,−1,…,12}|+1 = 16 (BCH-bound) [i]
  2. linear OA(256, 127, F2, 18) (dual of [127, 71, 19]-code), using the primitive narrow-sense BCH-code C(I) with length 127 = 27−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 19 [i]
  3. linear OA(264, 127, F2, 21) (dual of [127, 63, 22]-code), using the primitive cyclic code C(A) with length 127 = 27−1, defining set A = {0,1,3,5,7,9,11,13,15,63}, and minimum distance d ≥ |{−2,−1,…,18}|+1 = 22 (BCH-bound) [i]
  4. linear OA(242, 127, F2, 12) (dual of [127, 85, 13]-code), using the primitive narrow-sense BCH-code C(I) with length 127 = 27−1, defining interval I = [1,11], and designed minimum distance d ≥ |I|+1 = 13 [i]
  5. linear OA(21, 9, F2, 1) (dual of [9, 8, 2]-code), using
  6. linear OA(210, 22, F2, 5) (dual of [22, 12, 6]-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 OOA(275, 79, F2, 2, 20) (dual of [(79, 2), 83, 21]-NRT-code) [i]OOA Folding