MinT - Information on Result #3250170

Information on Result #3250170

Digital (70, 83, 1368)-net over F₂, using 2¹ times duplication based on digital (69, 82, 1368)-net over F₂, using

net defined by OOA [i] based on linear OOA(2⁸², 1368, F₂, 13, 13) (dual of [(1368, 13), 17702, 14]-NRT-code), using
- OOA 6-folding and stacking with additional row [i] based on linear OA(2⁸², 8209, F₂, 13) (dual of [8209, 8127, 14]-code), using
  - 2 times code embedding in larger space [i] based on linear OA(2⁸⁰, 8207, F₂, 13) (dual of [8207, 8127, 14]-code), using
    - constructionÂ X4 applied to C_e(12) âŠ‚ C_e(10) [i] based on
      1. linear OA(2⁷⁹, 8192, F₂, 13) (dual of [8192, 8113, 14]-code), using an extension C_e(12) of the primitive narrow-sense BCH-code C(I) with length 8191Â = 2¹³âˆ’1, defining interval IÂ =Â [1,12], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 13 [i]
      2. linear OA(2⁶⁶, 8192, F₂, 11) (dual of [8192, 8126, 12]-code), using an extension C_e(10) of the primitive narrow-sense BCH-code C(I) with length 8191Â = 2¹³âˆ’1, defining interval IÂ =Â [1,10], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 11 [i]
      3. linear OA(2¹⁴, 15, F₂, 13) (dual of [15, 1, 14]-code), using
        strength reduction [i] based on linear OA(2¹⁴, 15, F₂, 14) (dual of [15, 1, 15]-code or 15-arc in PG(13,2)), using
        dual of repetition code with length 15 [i]
      4. linear OA(2¹, 15, F₂, 1) (dual of [15, 14, 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, k and s, k and t, m and s, m and t, t and s.

Other Results with Identical Parameters

None.

Depending Results

None.