MinT - Information on Result #1750145

Information on Result #1750145

Digital (88, 101, 16389)-net over F₂, using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(2¹⁰¹, 16389, F₂, 4, 13) (dual of [(16389, 4), 65455, 14]-NRT-code), using

2¹ times duplication [i] based on linear OOA(2¹⁰⁰, 16389, F₂, 4, 13) (dual of [(16389, 4), 65456, 14]-NRT-code), using
- OOA 4-folding [i] based on linear OA(2¹⁰⁰, 65556, F₂, 13) (dual of [65556, 65456, 14]-code), using
  - 2 times code embedding in larger space [i] based on linear OA(2⁹⁸, 65554, F₂, 13) (dual of [65554, 65456, 14]-code), using
    - constructionÂ X4 applied to C_e(12) âŠ‚ C_e(10) [i] based on
      1. linear OA(2⁹⁷, 65536, F₂, 13) (dual of [65536, 65439, 14]-code), using an extension C_e(12) of the primitive narrow-sense BCH-code C(I) with length 65535Â = 2¹⁶âˆ’1, defining interval IÂ =Â [1,12], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 13 [i]
      2. linear OA(2⁸¹, 65536, F₂, 11) (dual of [65536, 65455, 12]-code), using an extension C_e(10) of the primitive narrow-sense BCH-code C(I) with length 65535Â = 2¹⁶âˆ’1, defining interval IÂ =Â [1,10], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 11 [i]
      3. linear OA(2¹⁷, 18, F₂, 17) (dual of [18, 1, 18]-code or 18-arc in PG(16,2)), using
        dual of repetition code with length 18 [i]
      4. 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: Linear.

Optimality

Show details for fixed k and m, k and s, k and t, m and s, m and t, t and s.

Other Results with Identical Parameters

None.

Depending Results

The following results depend on this result:

	Result		This result only	Method
1	Digital (89, 102, 16389)-net over F₂	[i]		Net Duplication