MinT - Information on Result #1166322

Information on Result #1166322

Linear OOA(2²¹⁷, 8197, F₂, 8, 27) (dual of [(8197, 8), 65359, 28]-NRT-code), using OOA 8-folding based on linear OA(2²¹⁷, 65576, F₂, 27) (dual of [65576, 65359, 28]-code), using

1 times code embedding in larger space [i] based on linear OA(2²¹⁶, 65575, F₂, 27) (dual of [65575, 65359, 28]-code), using
- constructionÂ X applied to C_e(26) âŠ‚ C_e(22) [i] based on
  1. linear OA(2²⁰⁹, 65536, F₂, 27) (dual of [65536, 65327, 28]-code), using an extension C_e(26) of the primitive narrow-sense BCH-code C(I) with length 65535Â = 2¹⁶âˆ’1, defining interval IÂ =Â [1,26], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 27 [i]
  2. 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]
  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(2²¹⁸, 8197, F₂, 8, 27) (dual of [(8197, 8), 65358, 28]-NRT-code)	[i]	OOA Duplication
2	Linear OOA(2²¹⁹, 8197, F₂, 8, 27) (dual of [(8197, 8), 65357, 28]-NRT-code)	[i]
3	Linear OOA(2²²⁰, 8197, F₂, 8, 27) (dual of [(8197, 8), 65356, 28]-NRT-code)	[i]
4	Linear OOA(2²¹⁶, 8196, F₂, 8, 26) (dual of [(8196, 8), 65352, 27]-NRT-code)	[i]	Truncation for OOAs