MinT - Information on Result #1199736

Information on Result #1199736

Digital (50, 70, 3286)-net over F₃₂, using net defined by OOA based on linear OOA(32⁷⁰, 3286, F₃₂, 22, 20) (dual of [(3286, 22), 72222, 21]-NRT-code), using

OOA 5-folding and stacking with additional row [i] based on linear OOA(32⁷⁰, 16431, F₃₂, 2, 20) (dual of [(16431, 2), 32792, 21]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(32¹¹, 44, F₃₂, 2, 10) (dual of [(44, 2), 77, 11]-NRT-code), using
    - extended algebraic-geometric NRT-code AG_e(2;F,77P) [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(32⁵⁹, 16387, F₃₂, 2, 20) (dual of [(16387, 2), 32715, 21]-NRT-code), using
    - OOA 2-folding [i] based on linear OA(32⁵⁹, 32774, F₃₂, 20) (dual of [32774, 32715, 21]-code), using
      - discarding factors / shortening the dual code based on linear OA(32⁵⁹, 32775, F₃₂, 20) (dual of [32775, 32716, 21]-code), using
        constructionÂ X applied to C_e(19) âŠ‚ C_e(17) [i] based on
        linear OA(32⁵⁸, 32768, F₃₂, 20) (dual of [32768, 32710, 21]-code), using an extension C_e(19) of the primitive narrow-sense BCH-code C(I) with length 32767Â = 32³âˆ’1, defining interval IÂ =Â [1,19], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 20 [i]
        linear OA(32⁵², 32768, F₃₂, 18) (dual of [32768, 32716, 19]-code), using an extension C_e(17) of the primitive narrow-sense BCH-code C(I) with length 32767Â = 32³âˆ’1, defining interval IÂ =Â [1,17], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 18 [i]
        linear OA(32¹, 7, F₃₂, 1) (dual of [7, 6, 2]-code), using
        discarding factors / shortening the dual code based on linear OA(32¹, s, F₃₂, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
        parity-check code [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.