MinT - Information on Result #1727178

Information on Result #1727178

Digital (60, 71, 1048607)-net over F₈, using net defined by OOA based on linear OOA(8⁷¹, 1048607, F₈, 15, 11) (dual of [(1048607, 15), 15729034, 12]-NRT-code), using

OOA 2-folding and stacking with additional row [i] based on linear OOA(8⁷¹, 2097215, F₈, 3, 11) (dual of [(2097215, 3), 6291574, 12]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(8⁷¹, 2097216, F₈, 3, 11) (dual of [(2097216, 3), 6291577, 12]-NRT-code), using
  - embedding of OOA with Gilbertâ€“VarÅ¡amov bound [i] based on linear OA(8⁷¹, 2097216, F₈, 11) (dual of [2097216, 2097145, 12]-code), using
    - (u,Â u+v)-construction [i] based on
      1. linear OA(8⁷, 57, F₈, 5) (dual of [57, 50, 6]-code), using
        a code by Danev and Olsson [i]
      2. linear OA(8⁶⁴, 2097159, F₈, 11) (dual of [2097159, 2097095, 12]-code), using
        constructionÂ X applied to C_e(10) âŠ‚ C_e(9) [i] based on
        linear OA(8⁶⁴, 2097152, F₈, 11) (dual of [2097152, 2097088, 12]-code), using an extension C_e(10) of the primitive narrow-sense BCH-code C(I) with length 2097151Â = 8⁷âˆ’1, defining interval IÂ =Â [1,10], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 11 [i]
        linear OA(8⁵⁷, 2097152, F₈, 10) (dual of [2097152, 2097095, 11]-code), using an extension C_e(9) of the primitive narrow-sense BCH-code C(I) with length 2097151Â = 8⁷âˆ’1, defining interval IÂ =Â [1,9], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 10 [i]
        linear OA(8⁰, 7, F₈, 0) (dual of [7, 7, 1]-code), using
        discarding factors / shortening the dual code based on linear OA(8⁰, s, F₈, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
        OA with only one run / dual of code without redundancy [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.