MinT - Information on Result #1832567

Information on Result #1832567

OOA(128⁶⁰, 33027, S₁₂₈, 2, 21), using (u,Â u+v)-construction based on

OOA(128¹³, 258, S₁₂₈, 2, 10), using
- extracting embedded OOA [i] based on (3, 13, 258)-net in base 128, using
  - 3 times m-reduction [i] based on (3, 16, 258)-net in base 128, using
    - base change [i] based on digital (1, 14, 258)-net over F₂₅₆, using
      - net from sequence [i] based on digital (1, 257)-sequence over F₂₅₆, using
        Niederreiter sequence [i]
OOA(128⁴⁷, 32769, S₁₂₈, 2, 21), using
- OOA 2-folding [i] based on OA(128⁴⁷, 65538, S₁₂₈, 21), using
  - discarding parts of the base [i] based on linear OA(256⁴¹, 65538, F₂₅₆, 21) (dual of [65538, 65497, 22]-code), using
    - constructionÂ X applied to C_e(20) âŠ‚ C_e(19) [i] based on
      1. linear OA(256⁴¹, 65536, F₂₅₆, 21) (dual of [65536, 65495, 22]-code), using an extension C_e(20) of the primitive narrow-sense BCH-code C(I) with length 65535Â = 256²âˆ’1, defining interval IÂ =Â [1,20], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 21 [i]
      2. linear OA(256³⁹, 65536, F₂₅₆, 20) (dual of [65536, 65497, 21]-code), using an extension C_e(19) of the primitive narrow-sense BCH-code C(I) with length 65535Â = 256²âˆ’1, defining interval IÂ =Â [1,19], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 20 [i]
      3. linear OA(256⁰, 2, F₂₅₆, 0) (dual of [2, 2, 1]-code), using
        discarding factors / shortening the dual code based on linear OA(256⁰, s, F₂₅₆, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
        OA with only one run / dual of code without redundancy [i]

Mode: Constructive.

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.