MinT - Information on Result #1194920

Information on Result #1194920

Digital (29, 38, 32777)-net over F₁₆, using net defined by OOA based on linear OOA(16³⁸, 32777, F₁₆, 10, 9) (dual of [(32777, 10), 327732, 10]-NRT-code), using

OOA 2-folding and stacking with additional row [i] based on linear OOA(16³⁸, 65555, F₁₆, 2, 9) (dual of [(65555, 2), 131072, 10]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(16⁴, 17, F₁₆, 2, 4) (dual of [(17, 2), 30, 5]-NRT-code), using
    - extended Reedâ€“Solomon NRT-code RS_e(2;30,16) [i]
  2. linear OOA(16³⁴, 65538, F₁₆, 2, 9) (dual of [(65538, 2), 131042, 10]-NRT-code), using
    - OOA 2-folding [i] based on linear OA(16³⁴, 131076, F₁₆, 9) (dual of [131076, 131042, 10]-code), using
      - trace code [i] based on linear OA(256¹⁷, 65538, F₂₅₆, 9) (dual of [65538, 65521, 10]-code), using
        constructionÂ X applied to C_e(8) âŠ‚ C_e(7) [i] based on
        linear OA(256¹⁷, 65536, F₂₅₆, 9) (dual of [65536, 65519, 10]-code), using an extension C_e(8) of the primitive narrow-sense BCH-code C(I) with length 65535Â = 256²âˆ’1, defining interval IÂ =Â [1,8], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 9 [i]
        linear OA(256¹⁵, 65536, F₂₅₆, 8) (dual of [65536, 65521, 9]-code), using an extension C_e(7) of the primitive narrow-sense BCH-code C(I) with length 65535Â = 256²âˆ’1, defining interval IÂ =Â [1,7], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 8 [i]
        linear OA(256⁰, 2, F₂₅₆, 0) (dual of [2, 2, 1]-code), using
        discarding factors / shortening the dual code based on linear OA(256⁰, s, F₂₅₆, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
        OA with only one run / dual of code without redundancy [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.