MinT - Information on Result #2922684

Information on Result #2922684

Linear OOA(2²⁵⁰, 10929, F₂, 6, 31) (dual of [(10929, 6), 65324, 32]-NRT-code), using 2² times duplication based on linear OOA(2²⁴⁸, 10929, F₂, 6, 31) (dual of [(10929, 6), 65326, 32]-NRT-code), using

OOA 6-folding [i] based on linear OA(2²⁴⁸, 65574, F₂, 31) (dual of [65574, 65326, 32]-code), using
- discarding factors / shortening the dual code based on linear OA(2²⁴⁸, 65575, F₂, 31) (dual of [65575, 65327, 32]-code), using
  - constructionÂ X applied to C_e(30) âŠ‚ C_e(26) [i] based on
    1. linear OA(2²⁴¹, 65536, F₂, 31) (dual of [65536, 65295, 32]-code), using an extension C_e(30) of the primitive narrow-sense BCH-code C(I) with length 65535Â = 2¹⁶âˆ’1, defining interval IÂ =Â [1,30], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 31 [i]
    2. 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]
    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(2²⁵⁰, 10929, F₂, 7, 31) (dual of [(10929, 7), 76253, 32]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
2	Linear OOA(2²⁵⁰, 10929, F₂, 8, 31) (dual of [(10929, 8), 87182, 32]-NRT-code)	[i]
3	Digital (219, 250, 10929)-net over F₂	[i]