MinT - Information on Result #1479873

Information on Result #1479873

Linear OOA(4²¹³, 27101, F₄, 3, 33) (dual of [(27101, 3), 81090, 34]-NRT-code), using OOA 2-folding based on linear OOA(4²¹³, 54202, F₄, 2, 33) (dual of [(54202, 2), 108191, 34]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(4²¹³, 54203, F₄, 2, 33) (dual of [(54203, 2), 108193, 34]-NRT-code), using
- embedding of OOA with Gilbertâ€“VarÅ¡amov bound [i] based on linear OA(4²¹³, 54203, F₄, 33) (dual of [54203, 53990, 34]-code), using
  - discarding factors / shortening the dual code based on linear OA(4²¹³, 65559, F₄, 33) (dual of [65559, 65346, 34]-code), using
    - (u,Â u+v)-construction [i] based on
      1. linear OA(4²⁰, 22, F₄, 16) (dual of [22, 2, 17]-code), using
        3 times truncation [i] based on linear OA(4²³, 25, F₄, 19) (dual of [25, 2, 20]-code), using
        repeating each code word 5 times [i] based on linear OA(4³, 5, F₄, 3) (dual of [5, 2, 4]-code or 5-arc in PG(2,4) or 5-cap in PG(2,4)), using
        extended Reedâ€“Solomon code RS_e(2,4) [i]
        Simplex code S(2,4) [i]
      2. linear OA(4¹⁹³, 65537, F₄, 33) (dual of [65537, 65344, 34]-code), using
        the expurgated narrow-sense BCH-code C(I) with length 65537Â | 4¹⁶âˆ’1, defining interval IÂ =Â [0,16], and minimum distance dÂ â‰¥ |{−16,−15,…,16}|+1Â =Â 34 (BCH-bound) [i]

Mode: Linear.

Optimality

Show details for fixed k and m, n and k, k and s, k and t, n and m, m and s, m and t, n and s, n and t.

Other Results with Identical Parameters

None.

Depending Results

None.