MinT - Information on Result #2417042

Information on Result #2417042

Linear OOA(2⁵⁷, 1030, F₂, 2, 10) (dual of [(1030, 2), 2003, 11]-NRT-code), using strength reduction based on linear OOA(2⁵⁷, 1030, F₂, 2, 11) (dual of [(1030, 2), 2003, 12]-NRT-code), using

OOA 2-folding [i] based on linear OA(2⁵⁷, 2060, F₂, 11) (dual of [2060, 2003, 12]-code), using
- constructionÂ X applied to C_e(10) âŠ‚ C_e(8) [i] based on
  1. linear OA(2⁵⁶, 2048, F₂, 11) (dual of [2048, 1992, 12]-code), using an extension C_e(10) of the primitive narrow-sense BCH-code C(I) with length 2047Â = 2¹¹âˆ’1, defining interval IÂ =Â [1,10], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 11 [i]
  2. linear OA(2⁴⁵, 2048, F₂, 9) (dual of [2048, 2003, 10]-code), using an extension C_e(8) of the primitive narrow-sense BCH-code C(I) with length 2047Â = 2¹¹âˆ’1, defining interval IÂ =Â [1,8], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 9 [i]
  3. linear OA(2¹, 12, F₂, 1) (dual of [12, 11, 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(2⁵⁷, 774, F₂, 3, 10) (dual of [(774, 3), 2265, 11]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
2	Linear OOA(2⁵⁷, 774, F₂, 4, 10) (dual of [(774, 4), 3039, 11]-NRT-code)	[i]
3	Linear OOA(2⁵⁷, 774, F₂, 5, 10) (dual of [(774, 5), 3813, 11]-NRT-code)	[i]
4	Linear OOA(2⁵⁷, 774, F₂, 6, 10) (dual of [(774, 6), 4587, 11]-NRT-code)	[i]
5	Linear OOA(2⁵⁷, 774, F₂, 7, 10) (dual of [(774, 7), 5361, 11]-NRT-code)	[i]
6	Linear OOA(2⁵⁷, 774, F₂, 8, 10) (dual of [(774, 8), 6135, 11]-NRT-code)	[i]
7	Digital (47, 57, 774)-net over F₂	[i]