MinT - Information on Result #1194988

Information on Result #1194988

Digital (44, 54, 209765)-net over F₁₆, using net defined by OOA based on linear OOA(16⁵⁴, 209765, F₁₆, 10, 10) (dual of [(209765, 10), 2097596, 11]-NRT-code), using

OA 5-folding and stacking [i] based on linear OA(16⁵⁴, 1048825, F₁₆, 10) (dual of [1048825, 1048771, 11]-code), using
- discarding factors / shortening the dual code based on linear OA(16⁵⁴, 1048829, F₁₆, 10) (dual of [1048829, 1048775, 11]-code), using
  - (u,Â u+v)-construction [i] based on
    1. linear OA(16⁷, 241, F₁₆, 5) (dual of [241, 234, 6]-code), using
      - a code by Danev and Olsson [i]
    2. linear OA(16⁴⁷, 1048588, F₁₆, 10) (dual of [1048588, 1048541, 11]-code), using
      - constructionÂ X4 applied to C_e(9) âŠ‚ C_e(7) [i] based on
        linear OA(16⁴⁶, 1048576, F₁₆, 10) (dual of [1048576, 1048530, 11]-code), using an extension C_e(9) of the primitive narrow-sense BCH-code C(I) with length 1048575Â = 16⁵âˆ’1, defining interval IÂ =Â [1,9], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 10 [i]
        linear OA(16³⁶, 1048576, F₁₆, 8) (dual of [1048576, 1048540, 9]-code), using an extension C_e(7) of the primitive narrow-sense BCH-code C(I) with length 1048575Â = 16⁵âˆ’1, defining interval IÂ =Â [1,7], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 8 [i]
        linear OA(16¹¹, 12, F₁₆, 11) (dual of [12, 1, 12]-code or 12-arc in PG(10,16)), using
        dual of repetition code with length 12 [i]
        linear OA(16¹, 12, F₁₆, 1) (dual of [12, 11, 2]-code), using
        discarding factors / shortening the dual code based on linear OA(16¹, 16, F₁₆, 1) (dual of [16, 15, 2]-code), using
        Reedâ€“Solomon code RS(15,16) [i]

Mode: Constructive and linear.

Optimality

Show details for fixed k and m, k and s, k and t, m and s, m and t, t and s.

Other Results with Identical Parameters

None.

Depending Results

None.