MinT - Information on Result #1200170

Information on Result #1200170

Digital (78, 110, 2053)-net over F₃₂, using net defined by OOA based on linear OOA(32¹¹⁰, 2053, F₃₂, 34, 32) (dual of [(2053, 34), 69692, 33]-NRT-code), using

OOA 8-folding and stacking with additional row [i] based on linear OOA(32¹¹⁰, 16425, F₃₂, 2, 32) (dual of [(16425, 2), 32740, 33]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(32¹¹⁰, 16427, F₃₂, 2, 32) (dual of [(16427, 2), 32744, 33]-NRT-code), using
  - (u,Â u+v)-construction [i] based on
    1. linear OOA(32¹⁷, 44, F₃₂, 2, 16) (dual of [(44, 2), 71, 17]-NRT-code), using
      - extended algebraic-geometric NRT-code AG_e(2;F,71P) [i] based on function field F/F₃₂ with g(F) = 1 and N(F) ≥ 44, using
        a function field by SÃ©mirat [i]
    2. linear OOA(32⁹³, 16383, F₃₂, 2, 32) (dual of [(16383, 2), 32673, 33]-NRT-code), using
      - OOA 2-folding [i] based on linear OA(32⁹³, 32766, F₃₂, 32) (dual of [32766, 32673, 33]-code), using
        discarding factors / shortening the dual code based on linear OA(32⁹³, 32767, F₃₂, 32) (dual of [32767, 32674, 33]-code), using
        1 times truncation [i] based on linear OA(32⁹⁴, 32768, F₃₂, 33) (dual of [32768, 32674, 34]-code), using
        an extension C_e(32) of the primitive narrow-sense BCH-code C(I) with length 32767Â = 32³âˆ’1, defining interval IÂ =Â [1,32], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 33 [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.