MinT - Information on Result #1743880

Information on Result #1743880

Digital (30, 43, 131105)-net over F₆₄, using net defined by OOA based on linear OOA(64⁴³, 131105, F₆₄, 15, 13) (dual of [(131105, 15), 1966532, 14]-NRT-code), using

OOA 2-folding and stacking with additional row [i] based on linear OOA(64⁴³, 262211, F₆₄, 3, 13) (dual of [(262211, 3), 786590, 14]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(64⁴³, 262212, F₆₄, 3, 13) (dual of [(262212, 3), 786593, 14]-NRT-code), using
  - embedding of OOA with Gilbertâ€“VarÅ¡amov bound [i] based on linear OA(64⁴³, 262212, F₆₄, 13) (dual of [262212, 262169, 14]-code), using
    - (u,Â u+v)-construction [i] based on
      1. linear OA(64⁶, 65, F₆₄, 6) (dual of [65, 59, 7]-code or 65-arc in PG(5,64)), using
        extended Reedâ€“Solomon code RS_e(59,64) [i]
      2. linear OA(64³⁷, 262147, F₆₄, 13) (dual of [262147, 262110, 14]-code), using
        constructionÂ X applied to C_e(12) âŠ‚ C_e(11) [i] based on
        linear OA(64³⁷, 262144, F₆₄, 13) (dual of [262144, 262107, 14]-code), using an extension C_e(12) of the primitive narrow-sense BCH-code C(I) with length 262143Â = 64³âˆ’1, defining interval IÂ =Â [1,12], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 13 [i]
        linear OA(64³⁴, 262144, F₆₄, 12) (dual of [262144, 262110, 13]-code), using an extension C_e(11) of the primitive narrow-sense BCH-code C(I) with length 262143Â = 64³âˆ’1, defining interval IÂ =Â [1,11], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 12 [i]
        linear OA(64⁰, 3, F₆₄, 0) (dual of [3, 3, 1]-code), using
        discarding factors / shortening the dual code based on linear OA(64⁰, s, F₆₄, 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.