MinT - Information on Result #894532

Information on Result #894532

Linear OOA(2⁶¹, 47, F₂, 2, 21) (dual of [(47, 2), 33, 22]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(2²¹, 23, F₂, 2, 10) (dual of [(23, 2), 25, 11]-NRT-code), using
- extracting embedded OOA [i] based on digital (11, 21, 23)-net over F₂, using
  - linear code embedding found in a computer search [i]
linear OOA(2⁴⁰, 24, F₂, 2, 21) (dual of [(24, 2), 8, 22]-NRT-code), using
- OOA 2-folding [i] based on linear OA(2⁴⁰, 48, F₂, 21) (dual of [48, 8, 22]-code), using
  - concatenation of two codes [i] based on
    1. linear OA(4¹², 16, F₄, 10) (dual of [16, 4, 11]-code), using
      - 1 times truncation [i] based on linear OA(4¹³, 17, F₄, 11) (dual of [17, 4, 12]-code), using
        projective code from ovoid in PG(3,Â 4) [i]
    2. linear OA(2¹, 3, F₂, 1) (dual of [3, 2, 2]-code), using
      - discarding factors / shortening the dual code based on linear OA(2¹, s, F₂, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
        parity-check code [i]

Mode: Constructive and linear.

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