MinT - Information on Result #1057574

Information on Result #1057574

Linear OOA(2¹³⁷, 36, F₂, 4, 80) (dual of [(36, 4), 7, 81]-NRT-code), using OOA 2-folding based on linear OOA(2¹³⁷, 72, F₂, 2, 80) (dual of [(72, 2), 7, 81]-NRT-code), using

juxtaposition [i] based on
1. linear OOA(2³⁷, 22, F₂, 2, 21) (dual of [(22, 2), 7, 22]-NRT-code), using
  - (u,Â u+v)-construction [i] based on
    1. linear OOA(2¹⁶, 11, F₂, 2, 10) (dual of [(11, 2), 6, 11]-NRT-code), using
      - extracting embedded OOA [i] based on digital (6, 16, 11)-net over F₂, using
        linear code embedding found in a computer search [i]
    2. linear OOA(2²¹, 11, F₂, 2, 21) (dual of [(11, 2), 1, 22]-NRT-code), using
      - dual of repetition NRT-code with length 11 [i]
2. linear OOA(2⁹³, 50, F₂, 2, 58) (dual of [(50, 2), 7, 59]-NRT-code), using
  - 1 step truncation [i] based on linear OOA(2⁹⁴, 51, F₂, 2, 59) (dual of [(51, 2), 8, 60]-NRT-code), using
    - concatenation of two NRT-codes [i] based on
      1. 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 OOA(2⁴, 3, F₂, 2, 4) (dual of [(3, 2), 2, 5]-NRT-code), using
        extended Reedâ€“Solomon NRT-code RS_e(2;2,2) [i]

Mode: Constructive and 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.