MinT - Information on Result #1749394

Information on Result #1749394

Digital (58, 70, 768)-net over F₂, using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(2⁷⁰, 768, F₂, 2, 12) (dual of [(768, 2), 1466, 13]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(2⁷⁰, 1031, F₂, 2, 12) (dual of [(1031, 2), 1992, 13]-NRT-code), using
- 2¹ times duplication [i] based on linear OOA(2⁶⁹, 1031, F₂, 2, 12) (dual of [(1031, 2), 1993, 13]-NRT-code), using
  - OOA 2-folding [i] based on linear OA(2⁶⁹, 2062, F₂, 12) (dual of [2062, 1993, 13]-code), using
    - strength reduction [i] based on linear OA(2⁶⁹, 2062, F₂, 13) (dual of [2062, 1993, 14]-code), using
      - adding a parity check bit [i] based on linear OA(2⁶⁸, 2061, F₂, 12) (dual of [2061, 1993, 13]-code), using
        constructionÂ X4 applied to C([0,12]) âŠ‚ C([1,10]) [i] based on
        linear OA(2⁶⁷, 2047, F₂, 13) (dual of [2047, 1980, 14]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 2047Â = 2¹¹âˆ’1, defining interval IÂ =Â [0,12], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 14 [i]
        linear OA(2⁵⁵, 2047, F₂, 10) (dual of [2047, 1992, 11]-code), using the primitive narrow-sense BCH-code C(I) with length 2047Â = 2¹¹âˆ’1, defining interval IÂ =Â [1,10], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 11 [i]
        linear OA(2¹³, 14, F₂, 13) (dual of [14, 1, 14]-code or 14-arc in PG(12,2)), using
        dual of repetition code with length 14 [i]
        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, k and s, k and t, m and s, m and t, t and s.

Other Results with Identical Parameters

None.

Depending Results

None.