MinT - Information on Result #807688

Information on Result #807688

Linear OOA(2¹⁵², 517, F₂, 2, 31) (dual of [(517, 2), 882, 32]-NRT-code), using OOA 2-folding based on linear OA(2¹⁵², 1034, F₂, 31) (dual of [1034, 882, 32]-code), using

discarding factors / shortening the dual code based on linear OA(2¹⁵², 1035, F₂, 31) (dual of [1035, 883, 32]-code), using
- constructionÂ X applied to C_e(30) âŠ‚ C_e(28) [i] based on
  1. linear OA(2¹⁵¹, 1024, F₂, 31) (dual of [1024, 873, 32]-code), using an extension C_e(30) of the primitive narrow-sense BCH-code C(I) with length 1023Â = 2¹⁰âˆ’1, defining interval IÂ =Â [1,30], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 31 [i]
  2. linear OA(2¹⁴¹, 1024, F₂, 29) (dual of [1024, 883, 30]-code), using an extension C_e(28) of the primitive narrow-sense BCH-code C(I) with length 1023Â = 2¹⁰âˆ’1, defining interval IÂ =Â [1,28], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 29 [i]
  3. linear OA(2¹, 11, F₂, 1) (dual of [11, 10, 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(2¹⁵², 424, F₂, 3, 31) (dual of [(424, 3), 1120, 32]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
2	Linear OOA(2¹⁵², 424, F₂, 4, 31) (dual of [(424, 4), 1544, 32]-NRT-code)	[i]
3	Linear OOA(2¹⁵², 424, F₂, 5, 31) (dual of [(424, 5), 1968, 32]-NRT-code)	[i]
4	Linear OOA(2¹⁵², 424, F₂, 6, 31) (dual of [(424, 6), 2392, 32]-NRT-code)	[i]
5	Linear OOA(2¹⁵², 424, F₂, 7, 31) (dual of [(424, 7), 2816, 32]-NRT-code)	[i]
6	Linear OOA(2¹⁵², 424, F₂, 8, 31) (dual of [(424, 8), 3240, 32]-NRT-code)	[i]
7	Digital (121, 152, 424)-net over F₂	[i]