MinT - Information on Result #3260360

Information on Result #3260360

Digital (101, 122, 7816)-net over F₅, using 5¹ times duplication based on digital (100, 121, 7816)-net over F₅, using

net defined by OOA [i] based on linear OOA(5¹²¹, 7816, F₅, 21, 21) (dual of [(7816, 21), 164015, 22]-NRT-code), using
- OOA 10-folding and stacking with additional row [i] based on linear OA(5¹²¹, 78161, F₅, 21) (dual of [78161, 78040, 22]-code), using
  - constructionÂ X applied to C_e(20) âŠ‚ C_e(15) [i] based on
    1. linear OA(5¹¹³, 78125, F₅, 21) (dual of [78125, 78012, 22]-code), using an extension C_e(20) of the primitive narrow-sense BCH-code C(I) with length 78124Â = 5⁷âˆ’1, defining interval IÂ =Â [1,20], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 21 [i]
    2. linear OA(5⁸⁵, 78125, F₅, 16) (dual of [78125, 78040, 17]-code), using an extension C_e(15) of the primitive narrow-sense BCH-code C(I) with length 78124Â = 5⁷âˆ’1, defining interval IÂ =Â [1,15], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 16 [i]
    3. linear OA(5⁸, 36, F₅, 4) (dual of [36, 28, 5]-code), using
      - discarding factors / shortening the dual code based on linear OA(5⁸, 52, F₅, 4) (dual of [52, 44, 5]-code), using
        trace code [i] based on linear OA(25⁴, 26, F₂₅, 4) (dual of [26, 22, 5]-code or 26-arc in PG(3,25)), using
        extended Reedâ€“Solomon code RS_e(22,25) [i]
        algebraic-geometric code AG(F, Q+9P) with degQ = 3 and degPÂ =Â 2 [i] based on function field F/F₂₅ with g(F) = 0 and N(F) ≥ 26, using the rational function field F₂₅(x) [i]
        algebraic-geometric code AG(F,7P) with degPÂ =Â 3 [i] based on function field F/F₂₅ with g(F) = 0 and N(F) ≥ 26 (see above)

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.