MinT - Information on Result #1051489

Information on Result #1051489

Linear OOA(2⁹², 8196, F₂, 4, 13) (dual of [(8196, 4), 32692, 14]-NRT-code), using OOA 4-folding based on linear OA(2⁹², 32784, F₂, 13) (dual of [32784, 32692, 14]-code), using

constructionÂ X applied to C_e(12) âŠ‚ C_e(10) [i] based on
1. linear OA(2⁹¹, 32768, F₂, 13) (dual of [32768, 32677, 14]-code), using an extension C_e(12) of the primitive narrow-sense BCH-code C(I) with length 32767Â = 2¹⁵âˆ’1, defining interval IÂ =Â [1,12], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 13 [i]
2. linear OA(2⁷⁶, 32768, F₂, 11) (dual of [32768, 32692, 12]-code), using an extension C_e(10) of the primitive narrow-sense BCH-code C(I) with length 32767Â = 2¹⁵âˆ’1, defining interval IÂ =Â [1,10], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 11 [i]
3. linear OA(2¹, 16, F₂, 1) (dual of [16, 15, 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.

Other Results with Identical Parameters

None.

Depending Results

The following results depend on this result:

	Result		Method
1	Linear OOA(2⁹², 8196, F₂, 4, 12) (dual of [(8196, 4), 32692, 13]-NRT-code)	[i]	Strength Reduction for OOAs
2	Linear OOA(2⁹³, 8196, F₂, 4, 13) (dual of [(8196, 4), 32691, 14]-NRT-code)	[i]	OOA Duplication
3	Linear OOA(2⁹⁴, 8196, F₂, 4, 13) (dual of [(8196, 4), 32690, 14]-NRT-code)	[i]	OOA Duplication
4	Linear OOA(2⁹², 7698, F₂, 5, 13) (dual of [(7698, 5), 38398, 14]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
5	Linear OOA(2⁹², 7698, F₂, 6, 13) (dual of [(7698, 6), 46096, 14]-NRT-code)	[i]
6	Linear OOA(2⁹², 7698, F₂, 7, 13) (dual of [(7698, 7), 53794, 14]-NRT-code)	[i]
7	Linear OOA(2⁹², 7698, F₂, 8, 13) (dual of [(7698, 8), 61492, 14]-NRT-code)	[i]
8	Digital (79, 92, 7698)-net over F₂	[i]