MinT - Information on Result #807116

Information on Result #807116

Linear OOA(2¹³¹, 517, F₂, 2, 26) (dual of [(517, 2), 903, 27]-NRT-code), using OOA 2-folding based on linear OA(2¹³¹, 1034, F₂, 26) (dual of [1034, 903, 27]-code), using

1 times truncation [i] 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(2¹³¹, 428, F₂, 3, 26) (dual of [(428, 3), 1153, 27]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
2	Linear OOA(2¹³¹, 428, F₂, 4, 26) (dual of [(428, 4), 1581, 27]-NRT-code)	[i]
3	Linear OOA(2¹³¹, 428, F₂, 5, 26) (dual of [(428, 5), 2009, 27]-NRT-code)	[i]
4	Linear OOA(2¹³¹, 428, F₂, 6, 26) (dual of [(428, 6), 2437, 27]-NRT-code)	[i]
5	Linear OOA(2¹³¹, 428, F₂, 7, 26) (dual of [(428, 7), 2865, 27]-NRT-code)	[i]
6	Linear OOA(2¹³¹, 428, F₂, 8, 26) (dual of [(428, 8), 3293, 27]-NRT-code)	[i]
7	Digital (105, 131, 428)-net over F₂	[i]