MinT - Information on Result #949853

Information on Result #949853

Linear OOA(2¹⁴⁴, 54, F₂, 3, 61) (dual of [(54, 3), 18, 62]-NRT-code), using OOA 3-folding based on linear OA(2¹⁴⁴, 162, F₂, 61) (dual of [162, 18, 62]-code), using

constructionÂ XX applied toC₃ âŠ‚ C₂ âŠ‚ C₁ [i] based on
1. linear OA(2¹²⁰, 127, F₂, 63) (dual of [127, 7, 64]-code), using code C₃ for uÂ =Â 7 by de Boer and Brouwer [i]
2. linear OA(2¹¹³, 127, F₂, 55) (dual of [127, 14, 56]-code), using code C₂ for uÂ =Â 7 by de Boer and Brouwer [i]
3. linear OA(2¹⁰⁶, 127, F₂, 47) (dual of [127, 21, 48]-code), using code C₁ for uÂ =Â 7 by de Boer and Brouwer [i]
4. linear OA(2¹², 23, F₂, 7) (dual of [23, 11, 8]-code), using
  - discarding factors / shortening the dual code based on linear OA(2¹², 24, F₂, 7) (dual of [24, 12, 8]-code), using
    - extended Golay code G_e(2) [i]
5. linear OA(2⁸, 12, F₂, 5) (dual of [12, 4, 6]-code), using
  - a code of Belov type defined by PG(3,2) ∖ PG(1,2) [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.