Information on Result #700662

Linear OA(2136, 156, F2, 58) (dual of [156, 20, 59]-code), using construction XX applied to C1 = C({0,1,3,5,7,9,11,13,15,19,21,23,27,29,31,43,63}), C2 = C([1,47]), C3 = C1 + C2 = C([1,43]), and C∩ = C1 ∩ C2 = C({0,1,3,5,7,9,11,13,15,19,21,23,27,29,31,43,47,63}) based on
  1. linear OA(2113, 127, F2, 51) (dual of [127, 14, 52]-code), using the primitive cyclic code C(A) with length 127 = 27−1, defining set A = {0,1,3,5,7,9,11,13,15,19,21,23,27,29,31,43,63}, and minimum distance d ≥ |{−4,−3,…,46}|+1 = 52 (BCH-bound) [i]
  2. linear OA(2112, 127, F2, 54) (dual of [127, 15, 55]-code), using the primitive narrow-sense BCH-code C(I) with length 127 = 27−1, defining interval I = [1,47], and designed minimum distance d ≥ |I|+1 = 55 [i]
  3. linear OA(2120, 127, F2, 63) (dual of [127, 7, 64]-code), using the primitive cyclic code C(A) with length 127 = 27−1, defining set A = {0,1,3,5,7,9,11,13,15,19,21,23,27,29,31,43,47,63}, and minimum distance d ≥ |{0,9,18,…,50}|+1 = 64 (BCH-bound) [i]
  4. linear OA(2105, 127, F2, 46) (dual of [127, 22, 47]-code), using the primitive narrow-sense BCH-code C(I) with length 127 = 27−1, defining interval I = [1,43], and designed minimum distance d ≥ |I|+1 = 47 [i]
  5. linear OA(25, 13, F2, 3) (dual of [13, 8, 4]-code or 13-cap in PG(4,2)), using
  6. linear OA(211, 16, F2, 7) (dual of [16, 5, 8]-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(2136, 78, F2, 2, 58) (dual of [(78, 2), 20, 59]-NRT-code) [i]OOA Folding
2Linear OOA(2136, 52, F2, 3, 58) (dual of [(52, 3), 20, 59]-NRT-code) [i]