Information on Result #700604

Linear OA(275, 157, F2, 21) (dual of [157, 82, 22]-code), using construction XX applied to C1 = C({0,1,3,5,7,9,11,63}), C2 = C([0,15]), C3 = C1 + C2 = C([0,11]), 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(257, 127, F2, 19) (dual of [127, 70, 20]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 127 = 27−1, defining interval I = [0,15], and designed minimum distance d ≥ |I|+1 = 20 [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(243, 127, F2, 13) (dual of [127, 84, 14]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 127 = 27−1, defining interval I = [0,11], and designed minimum distance d ≥ |I|+1 = 14 [i]
  5. linear OA(21, 8, F2, 1) (dual of [8, 7, 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 OA(274, 156, F2, 20) (dual of [156, 82, 21]-code) [i]Truncation
2Linear OOA(275, 78, F2, 2, 21) (dual of [(78, 2), 81, 22]-NRT-code) [i]OOA Folding
3Linear OOA(275, 52, F2, 3, 21) (dual of [(52, 3), 81, 22]-NRT-code) [i]