MinT - Information on Result #2922571

Information on Result #2922571

Linear OOA(2²⁵⁹, 21848, F₂, 6, 30) (dual of [(21848, 6), 130829, 31]-NRT-code), using 2³ times duplication based on linear OOA(2²⁵⁶, 21848, F₂, 6, 30) (dual of [(21848, 6), 130832, 31]-NRT-code), using

OOA 6-folding [i] based on linear OA(2²⁵⁶, 131088, F₂, 30) (dual of [131088, 130832, 31]-code), using
- discarding factors / shortening the dual code based on linear OA(2²⁵⁶, 131089, F₂, 30) (dual of [131089, 130833, 31]-code), using
  - 1 times truncation [i] based on linear OA(2²⁵⁷, 131090, F₂, 31) (dual of [131090, 130833, 32]-code), using
    - constructionÂ X applied to C_e(30) âŠ‚ C_e(28) [i] based on
      1. linear OA(2²⁵⁶, 131072, F₂, 31) (dual of [131072, 130816, 32]-code), using an extension C_e(30) of the primitive narrow-sense BCH-code C(I) with length 131071Â = 2¹⁷âˆ’1, defining interval IÂ =Â [1,30], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 31 [i]
      2. linear OA(2²³⁹, 131072, F₂, 29) (dual of [131072, 130833, 30]-code), using an extension C_e(28) of the primitive narrow-sense BCH-code C(I) with length 131071Â = 2¹⁷âˆ’1, defining interval IÂ =Â [1,28], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 29 [i]
      3. linear OA(2¹, 18, F₂, 1) (dual of [18, 17, 2]-code), using
        discarding factors / shortening the dual code based on linear OA(2¹, s, F₂, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
        parity-check code [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(2²⁵⁹, 19277, F₂, 7, 30) (dual of [(19277, 7), 134680, 31]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
2	Linear OOA(2²⁵⁹, 19277, F₂, 8, 30) (dual of [(19277, 8), 153957, 31]-NRT-code)	[i]
3	Digital (229, 259, 19277)-net over F₂	[i]