MinT - Information on Result #1151746

Information on Result #1151746

Linear OOA(2²⁵³, 599194, F₂, 7, 23) (dual of [(599194, 7), 4194105, 24]-NRT-code), using OOA 7-folding based on linear OA(2²⁵³, 4194358, F₂, 23) (dual of [4194358, 4194105, 24]-code), using

3 times code embedding in larger space [i] based on linear OA(2²⁵⁰, 4194355, F₂, 23) (dual of [4194355, 4194105, 24]-code), using
- constructionÂ X applied to C_e(22) âŠ‚ C_e(18) [i] based on
  1. linear OA(2²⁴³, 4194304, F₂, 23) (dual of [4194304, 4194061, 24]-code), using an extension C_e(22) of the primitive narrow-sense BCH-code C(I) with length 4194303Â = 2²²âˆ’1, defining interval IÂ =Â [1,22], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 23 [i]
  2. linear OA(2¹⁹⁹, 4194304, F₂, 19) (dual of [4194304, 4194105, 20]-code), using an extension C_e(18) of the primitive narrow-sense BCH-code C(I) with length 4194303Â = 2²²âˆ’1, defining interval IÂ =Â [1,18], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 19 [i]
  3. linear OA(2⁷, 51, F₂, 3) (dual of [51, 44, 4]-code or 51-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(2²⁵², 599193, F₂, 7, 22) (dual of [(599193, 7), 4194099, 23]-NRT-code)	[i]	Truncation for OOAs
2	Linear OOA(2²⁵³, 555446, F₂, 8, 23) (dual of [(555446, 8), 4443315, 24]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
3	Digital (230, 253, 555446)-net over F₂	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound