MinT - Information on Result #807230

Information on Result #807230

Linear OOA(2¹³², 517, F₂, 2, 27) (dual of [(517, 2), 902, 28]-NRT-code), using OOA 2-folding based on linear OA(2¹³², 1034, F₂, 27) (dual of [1034, 902, 28]-code), using

discarding factors / shortening the dual code based on linear OA(2¹³², 1035, F₂, 27) (dual of [1035, 903, 28]-code), using
- constructionÂ X applied to C_e(26) âŠ‚ C_e(24) [i] based on
  1. linear OA(2¹³¹, 1024, F₂, 27) (dual of [1024, 893, 28]-code), using an extension C_e(26) of the primitive narrow-sense BCH-code C(I) with length 1023Â = 2¹⁰âˆ’1, defining interval IÂ =Â [1,26], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 27 [i]
  2. linear OA(2¹²¹, 1024, F₂, 25) (dual of [1024, 903, 26]-code), using an extension C_e(24) of the primitive narrow-sense BCH-code C(I) with length 1023Â = 2¹⁰âˆ’1, defining interval IÂ =Â [1,24], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 25 [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(2¹³², 385, F₂, 3, 27) (dual of [(385, 3), 1023, 28]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
2	Linear OOA(2¹³², 385, F₂, 4, 27) (dual of [(385, 4), 1408, 28]-NRT-code)	[i]
3	Linear OOA(2¹³², 385, F₂, 5, 27) (dual of [(385, 5), 1793, 28]-NRT-code)	[i]
4	Linear OOA(2¹³², 385, F₂, 6, 27) (dual of [(385, 6), 2178, 28]-NRT-code)	[i]
5	Linear OOA(2¹³², 385, F₂, 7, 27) (dual of [(385, 7), 2563, 28]-NRT-code)	[i]
6	Linear OOA(2¹³², 385, F₂, 8, 27) (dual of [(385, 8), 2948, 28]-NRT-code)	[i]
7	Digital (105, 132, 385)-net over F₂	[i]