MinT - Information on Result #809073

Information on Result #809073

Linear OOA(2²¹⁷, 517, F₂, 2, 45) (dual of [(517, 2), 817, 46]-NRT-code), using OOA 2-folding based on linear OA(2²¹⁷, 1034, F₂, 45) (dual of [1034, 817, 46]-code), using

discarding factors / shortening the dual code based on linear OA(2²¹⁷, 1035, F₂, 45) (dual of [1035, 818, 46]-code), using
- constructionÂ X applied to C_e(44) âŠ‚ C_e(42) [i] based on
  1. linear OA(2²¹⁶, 1024, F₂, 45) (dual of [1024, 808, 46]-code), using an extension C_e(44) of the primitive narrow-sense BCH-code C(I) with length 1023Â = 2¹⁰âˆ’1, defining interval IÂ =Â [1,44], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 45 [i]
  2. linear OA(2²⁰⁶, 1024, F₂, 43) (dual of [1024, 818, 44]-code), using an extension C_e(42) of the primitive narrow-sense BCH-code C(I) with length 1023Â = 2¹⁰âˆ’1, defining interval IÂ =Â [1,42], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 43 [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(2²¹⁷, 516, F₂, 3, 45) (dual of [(516, 3), 1331, 46]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
2	Linear OOA(2²¹⁷, 516, F₂, 4, 45) (dual of [(516, 4), 1847, 46]-NRT-code)	[i]
3	Linear OOA(2²¹⁷, 516, F₂, 5, 45) (dual of [(516, 5), 2363, 46]-NRT-code)	[i]
4	Linear OOA(2²¹⁷, 516, F₂, 6, 45) (dual of [(516, 6), 2879, 46]-NRT-code)	[i]
5	Linear OOA(2²¹⁷, 516, F₂, 7, 45) (dual of [(516, 7), 3395, 46]-NRT-code)	[i]
6	Linear OOA(2²¹⁷, 516, F₂, 8, 45) (dual of [(516, 8), 3911, 46]-NRT-code)	[i]
7	Digital (172, 217, 516)-net over F₂	[i]