MinT - Information on Result #1686730

Information on Result #1686730

Linear OOA(2²²², 2051, F₂, 7, 34) (dual of [(2051, 7), 14135, 35]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(2²²², 2051, F₂, 4, 34) (dual of [(2051, 4), 7982, 35]-NRT-code), using

OOA 4-folding [i] based on linear OA(2²²², 8204, F₂, 34) (dual of [8204, 7982, 35]-code), using
- discarding factors / shortening the dual code based on linear OA(2²²², 8205, F₂, 34) (dual of [8205, 7983, 35]-code), using
  - 1 times truncation [i] based on linear OA(2²²³, 8206, F₂, 35) (dual of [8206, 7983, 36]-code), using
    - constructionÂ X applied to C_e(34) âŠ‚ C_e(32) [i] based on
      1. linear OA(2²²², 8192, F₂, 35) (dual of [8192, 7970, 36]-code), using an extension C_e(34) of the primitive narrow-sense BCH-code C(I) with length 8191Â = 2¹³âˆ’1, defining interval IÂ =Â [1,34], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 35 [i]
      2. linear OA(2²⁰⁹, 8192, F₂, 33) (dual of [8192, 7983, 34]-code), using an extension C_e(32) of the primitive narrow-sense BCH-code C(I) with length 8191Â = 2¹³âˆ’1, defining interval IÂ =Â [1,32], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 33 [i]
      3. linear OA(2¹, 14, F₂, 1) (dual of [14, 13, 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: 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		This result only	Method
1	Linear OOA(2²²³, 2051, F₂, 7, 34) (dual of [(2051, 7), 14134, 35]-NRT-code)	[i]		OOA Duplication
2	Linear OOA(2²²⁴, 2051, F₂, 7, 34) (dual of [(2051, 7), 14133, 35]-NRT-code)	[i]		OOA Duplication