MinT - Information on Result #3323487

Information on Result #3323487

Digital (78, 89, 32773)-net over F₂, using 2¹ times duplication based on digital (77, 88, 32773)-net over F₂, using

embedding of OOA with Gilbertâ€“VarÅ¡amov bound [i] based on linear OOA(2⁸⁸, 32773, F₂, 4, 11) (dual of [(32773, 4), 131004, 12]-NRT-code), using
- OOA 4-folding [i] based on linear OA(2⁸⁸, 131092, F₂, 11) (dual of [131092, 131004, 12]-code), using
  - 1 times code embedding in larger space [i] based on linear OA(2⁸⁷, 131091, F₂, 11) (dual of [131091, 131004, 12]-code), using
    - constructionÂ X4 applied to C_e(10) âŠ‚ C_e(8) [i] based on
      1. linear OA(2⁸⁶, 131072, F₂, 11) (dual of [131072, 130986, 12]-code), using an extension C_e(10) of the primitive narrow-sense BCH-code C(I) with length 131071Â = 2¹⁷âˆ’1, defining interval IÂ =Â [1,10], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 11 [i]
      2. linear OA(2⁶⁹, 131072, F₂, 9) (dual of [131072, 131003, 10]-code), using an extension C_e(8) of the primitive narrow-sense BCH-code C(I) with length 131071Â = 2¹⁷âˆ’1, defining interval IÂ =Â [1,8], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 9 [i]
      3. linear OA(2¹⁸, 19, F₂, 17) (dual of [19, 1, 18]-code), using
        strength reduction [i] based on linear OA(2¹⁸, 19, F₂, 18) (dual of [19, 1, 19]-code or 19-arc in PG(17,2)), using
        dual of repetition code with length 19 [i]
      4. linear OA(2¹, 19, F₂, 1) (dual of [19, 18, 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.