MinT - Information on Result #1837210

Information on Result #1837210

OOA(128⁷⁸, 22105, S₁₂₈, 3, 27), using (u,Â u+v)-construction based on

OOA(128¹⁶, 258, S₁₂₈, 3, 13), using
- extracting embedded OOA [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(128⁶², 21847, S₁₂₈, 3, 27), using
- OOA 3-folding [i] based on OA(128⁶², 65541, S₁₂₈, 27), using
  - discarding factors based on OA(128⁶², 65542, S₁₂₈, 27), using
    - discarding parts of the base [i] based on linear OA(256⁵⁴, 65542, F₂₅₆, 27) (dual of [65542, 65488, 28]-code), using
      - constructionÂ X applied to C([0,13]) âŠ‚ C([0,12]) [i] based on
        linear OA(256⁵³, 65537, F₂₅₆, 27) (dual of [65537, 65484, 28]-code), using the expurgated narrow-sense BCH-code C(I) with length 65537Â | 256⁴âˆ’1, defining interval IÂ =Â [0,13], and minimum distance dÂ â‰¥ |{−13,−12,…,13}|+1Â =Â 28 (BCH-bound) [i]
        linear OA(256⁴⁹, 65537, F₂₅₆, 25) (dual of [65537, 65488, 26]-code), using the expurgated narrow-sense BCH-code C(I) with length 65537Â | 256⁴âˆ’1, defining interval IÂ =Â [0,12], and minimum distance dÂ â‰¥ |{−12,−11,…,12}|+1Â =Â 26 (BCH-bound) [i]
        linear OA(256¹, 5, F₂₅₆, 1) (dual of [5, 4, 2]-code), using
        discarding factors / shortening the dual code based on linear OA(256¹, s, F₂₅₆, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
        parity-check code [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.