MinT - Information on Result #629306

Information on Result #629306

Linear OA(2¹⁴¹, 195, F₂, 45) (dual of [195, 54, 46]-code), using concatenation of two codes based on

linear OA(4³⁸, 65, F₄, 22) (dual of [65, 27, 23]-code), using
- the BCH-code C(I) with length 65Â | 4⁶âˆ’1, defining interval IÂ =Â {1,4,7,…,64}, and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 23 [i]
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 OA(2¹⁴¹, 195, F₂, 44) (dual of [195, 54, 45]-code)	[i]		Strength Reduction
2	Linear OA(2¹⁴², 196, F₂, 45) (dual of [196, 54, 46]-code)	[i]		Code Embedding in Larger Space
3	Linear OA(2¹⁴⁰, 194, F₂, 44) (dual of [194, 54, 45]-code)	[i]		Truncation
4	Linear OOA(2¹⁴¹, 97, F₂, 2, 45) (dual of [(97, 2), 53, 46]-NRT-code)	[i]		OOA Folding
5	Linear OOA(2¹⁴¹, 65, F₂, 3, 45) (dual of [(65, 3), 54, 46]-NRT-code)	[i]		OOA Folding