MinT - Information on Result #2222735

Information on Result #2222735

Linear OA(2¹⁵⁹, 173, F₂, 74) (dual of [173, 14, 75]-code), using 1 times truncation based on linear OA(2¹⁶⁰, 174, F₂, 75) (dual of [174, 14, 76]-code), using

concatenation of two codes [i] based on
1. linear OA(4⁵¹, 58, F₄, 37) (dual of [58, 7, 38]-code), using
  - discarding factors / shortening the dual code based on linear OA(4⁵¹, 59, F₄, 37) (dual of [59, 8, 38]-code), using
    - 6 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(2¹⁵⁹, 86, F₂, 2, 74) (dual of [(86, 2), 13, 75]-NRT-code)	[i]		OOA Folding
2	Linear OOA(2¹⁵⁹, 57, F₂, 3, 74) (dual of [(57, 3), 12, 75]-NRT-code)	[i]		OOA Folding