MinT - Information on Result #2222595

Information on Result #2222595

Linear OA(2¹¹⁷, 197, F₂, 34) (dual of [197, 80, 35]-code), using 1 times truncation based on linear OA(2¹¹⁸, 198, F₂, 35) (dual of [198, 80, 36]-code), using

concatenation of two codes [i] based on
1. linear OA(32¹⁷, 33, F₃₂, 17) (dual of [33, 16, 18]-code or 33-arc in PG(16,32)), using
  - extended Reedâ€“Solomon code RS_e(16,32) [i]
  - the expurgated narrow-sense BCH-code C(I) with length 33Â | 32²âˆ’1, defining interval IÂ =Â [0,8], and minimum distance dÂ â‰¥ |{−8,−7,…,8}|+1Â =Â 18 (BCH-bound) [i]
2. linear OA(2¹, 6, F₂, 1) (dual of [6, 5, 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		Method
1	Linear OA(2¹¹⁹, 199, F₂, 34) (dual of [199, 80, 35]-code)	[i]	Code Embedding in Larger Space
2	Linear OA(2¹²⁰, 200, F₂, 34) (dual of [200, 80, 35]-code)	[i]
3	Linear OA(2¹²¹, 201, F₂, 34) (dual of [201, 80, 35]-code)	[i]
4	Linear OA(2¹²¹, 202, F₂, 34) (dual of [202, 81, 35]-code)	[i]	ConstructionÂ X with VarÅ¡amov Bound
5	Linear OOA(2¹¹⁷, 98, F₂, 2, 34) (dual of [(98, 2), 79, 35]-NRT-code)	[i]	OOA Folding
6	Linear OOA(2¹¹⁷, 65, F₂, 3, 34) (dual of [(65, 3), 78, 35]-NRT-code)	[i]	OOA Folding