MinT - Information on Result #2865617

Information on Result #2865617

Linear OOA(2¹⁸⁷, 13115, F₂, 5, 23) (dual of [(13115, 5), 65388, 24]-NRT-code), using 2³ times duplication based on linear OOA(2¹⁸⁴, 13115, F₂, 5, 23) (dual of [(13115, 5), 65391, 24]-NRT-code), using

OOA 5-folding [i] based on linear OA(2¹⁸⁴, 65575, F₂, 23) (dual of [65575, 65391, 24]-code), using
- constructionÂ X applied to C_e(22) âŠ‚ C_e(18) [i] based on
  1. linear OA(2¹⁷⁷, 65536, F₂, 23) (dual of [65536, 65359, 24]-code), using an extension C_e(22) of the primitive narrow-sense BCH-code C(I) with length 65535Â = 2¹⁶âˆ’1, defining interval IÂ =Â [1,22], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 23 [i]
  2. linear OA(2¹⁴⁵, 65536, F₂, 19) (dual of [65536, 65391, 20]-code), using an extension C_e(18) of the primitive narrow-sense BCH-code C(I) with length 65535Â = 2¹⁶âˆ’1, defining interval IÂ =Â [1,18], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 19 [i]
  3. linear OA(2⁷, 39, F₂, 3) (dual of [39, 32, 4]-code or 39-cap in PG(6,2)), using
    - discarding factors / shortening the dual code based on linear OA(2⁷, 63, F₂, 3) (dual of [63, 56, 4]-code or 63-cap in PG(6,2)), using
      - the primitive expurgated narrow-sense BCH-code C(I) with length 63Â = 2⁶âˆ’1, defining interval IÂ =Â [0,1], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 4 [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(2¹⁸⁷, 11963, F₂, 6, 23) (dual of [(11963, 6), 71591, 24]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
2	Linear OOA(2¹⁸⁷, 11963, F₂, 7, 23) (dual of [(11963, 7), 83554, 24]-NRT-code)	[i]
3	Linear OOA(2¹⁸⁷, 11963, F₂, 8, 23) (dual of [(11963, 8), 95517, 24]-NRT-code)	[i]
4	Digital (164, 187, 11963)-net over F₂	[i]