MinT - Information on Result #2180107

Information on Result #2180107

Linear OA(2¹⁵², 168, F₂, 68) (dual of [168, 16, 69]-code), using strength reduction based on linear OA(2¹⁵², 168, F₂, 69) (dual of [168, 16, 70]-code), using

concatenation of two codes [i] based on
1. linear OA(4⁴⁸, 56, F₄, 34) (dual of [56, 8, 35]-code), using
  - 9 times truncation [i] based on linear OA(4⁵⁷, 65, F₄, 43) (dual of [65, 8, 44]-code), using
    - the expurgated narrow-sense BCH-code C(I) with length 65Â | 4⁶âˆ’1, defining interval IÂ =Â [0,21], and minimum distance dÂ â‰¥ |{−21,−20,…,21}|+1Â =Â 44 (BCH-bound) [i]
2. linear OA(2¹, 3, F₂, 1) (dual of [3, 2, 2]-code), using
  - discarding factors / shortening the dual code based on linear OA(2¹, s, F₂, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
    - parity-check code [i]

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:

	Result		This result only	Method
1	Linear OOA(2¹⁵², 84, F₂, 2, 68) (dual of [(84, 2), 16, 69]-NRT-code)	[i]		OOA Folding
2	Linear OOA(2¹⁵², 56, F₂, 3, 68) (dual of [(56, 3), 16, 69]-NRT-code)	[i]		OOA Folding