MinT - Information on Result #2915411

Information on Result #2915411

Linear OOA(2²⁴², 43697, F₂, 6, 26) (dual of [(43697, 6), 261940, 27]-NRT-code), using strength reduction based on linear OOA(2²⁴², 43697, F₂, 6, 27) (dual of [(43697, 6), 261940, 28]-NRT-code), using

OOA 6-folding [i] based on linear OA(2²⁴², 262182, F₂, 27) (dual of [262182, 261940, 28]-code), using
- discarding factors / shortening the dual code based on linear OA(2²⁴², 262187, F₂, 27) (dual of [262187, 261945, 28]-code), using
  - constructionÂ X applied to C_e(26) âŠ‚ C_e(22) [i] based on
    1. linear OA(2²³⁵, 262144, F₂, 27) (dual of [262144, 261909, 28]-code), using an extension C_e(26) of the primitive narrow-sense BCH-code C(I) with length 262143Â = 2¹⁸âˆ’1, defining interval IÂ =Â [1,26], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 27 [i]
    2. linear OA(2¹⁹⁹, 262144, F₂, 23) (dual of [262144, 261945, 24]-code), using an extension C_e(22) of the primitive narrow-sense BCH-code C(I) with length 262143Â = 2¹⁸âˆ’1, defining interval IÂ =Â [1,22], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 23 [i]
    3. linear OA(2⁷, 43, F₂, 3) (dual of [43, 36, 4]-code or 43-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(2²⁴², 43456, F₂, 7, 26) (dual of [(43456, 7), 303950, 27]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
2	Linear OOA(2²⁴², 43456, F₂, 8, 26) (dual of [(43456, 8), 347406, 27]-NRT-code)	[i]
3	Digital (216, 242, 43456)-net over F₂	[i]