MinT - Information on Result #1629564

Information on Result #1629564

Linear OOA(2³³, 132, F₂, 5, 8) (dual of [(132, 5), 627, 9]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(2³³, 132, F₂, 2, 8) (dual of [(132, 2), 231, 9]-NRT-code), using

OOA 2-folding [i] based on linear OA(2³³, 264, F₂, 8) (dual of [264, 231, 9]-code), using
- discarding factors / shortening the dual code based on linear OA(2³³, 265, F₂, 8) (dual of [265, 232, 9]-code), using
  - 1 times truncation [i] based on linear OA(2³⁴, 266, F₂, 9) (dual of [266, 232, 10]-code), using
    - constructionÂ X4 applied to C_e(8) âŠ‚ C_e(6) [i] based on
      1. linear OA(2³³, 256, F₂, 9) (dual of [256, 223, 10]-code), using an extension C_e(8) of the primitive narrow-sense BCH-code C(I) with length 255Â = 2⁸âˆ’1, defining interval IÂ =Â [1,8], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 9 [i]
      2. linear OA(2²⁵, 256, F₂, 7) (dual of [256, 231, 8]-code), using an extension C_e(6) of the primitive narrow-sense BCH-code C(I) with length 255Â = 2⁸âˆ’1, defining interval IÂ =Â [1,6], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 7 [i]
      3. linear OA(2⁹, 10, F₂, 9) (dual of [10, 1, 10]-code or 10-arc in PG(8,2)), using
        dual of repetition code with length 10 [i]
      4. linear OA(2¹, 10, F₂, 1) (dual of [10, 9, 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(2²¹⁸, 1677852, F₂, 5, 17) (dual of [(1677852, 5), 8389042, 18]-NRT-code)	[i]		(u,Â u+v)-Construction for OOAs