MinT - Information on Result #2866478

Information on Result #2866478

Linear OOA(2²³⁶, 6561, F₂, 5, 31) (dual of [(6561, 5), 32569, 32]-NRT-code), using 2³ times duplication based on linear OOA(2²³³, 6561, F₂, 5, 31) (dual of [(6561, 5), 32572, 32]-NRT-code), using

OOA 5-folding [i] based on linear OA(2²³³, 32805, F₂, 31) (dual of [32805, 32572, 32]-code), using
- constructionÂ X applied to C_e(30) âŠ‚ C_e(26) [i] based on
  1. linear OA(2²²⁶, 32768, F₂, 31) (dual of [32768, 32542, 32]-code), using an extension C_e(30) of the primitive narrow-sense BCH-code C(I) with length 32767Â = 2¹⁵âˆ’1, defining interval IÂ =Â [1,30], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 31 [i]
  2. linear OA(2¹⁹⁶, 32768, F₂, 27) (dual of [32768, 32572, 28]-code), using an extension C_e(26) of the primitive narrow-sense BCH-code C(I) with length 32767Â = 2¹⁵âˆ’1, defining interval IÂ =Â [1,26], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 27 [i]
  3. linear OA(2⁷, 37, F₂, 3) (dual of [37, 30, 4]-code or 37-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(2²³⁶, 6117, F₂, 6, 31) (dual of [(6117, 6), 36466, 32]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
2	Linear OOA(2²³⁶, 6117, F₂, 7, 31) (dual of [(6117, 7), 42583, 32]-NRT-code)	[i]
3	Linear OOA(2²³⁶, 6117, F₂, 8, 31) (dual of [(6117, 8), 48700, 32]-NRT-code)	[i]
4	Digital (205, 236, 6117)-net over F₂	[i]