MinT - Information on Result #1195854

Information on Result #1195854

Digital (21, 26, 4882949)-net over F₂₅, using net defined by OOA based on linear OOA(25²⁶, 4882949, F₂₅, 6, 5) (dual of [(4882949, 6), 29297668, 6]-NRT-code), using

OOA stacking with additional row [i] based on linear OOA(25²⁶, 4882950, F₂₅, 2, 5) (dual of [(4882950, 2), 9765874, 6]-NRT-code), using
- generalized (u,Â u+v)-construction [i] based on
  1. linear OOA(25⁰, 195318, F₂₅, 2, 0) (dual of [(195318, 2), 390636, 1]-NRT-code), using
    - discarding factors / shortening the dual code based on linear OOA(25⁰, s, F₂₅, 2, 0) for arbitrarily large s, using
      - OOA with only one run / dual of NRT-code without redundancy [i]
  2. linear OOA(25⁰, 195318, F₂₅, 2, 0) (dual of [(195318, 2), 390636, 1]-NRT-code) (see above)
  3. linear OOA(25⁰, 195318, F₂₅, 2, 0) (dual of [(195318, 2), 390636, 1]-NRT-code) (see above)
  4. linear OOA(25⁰, 195318, F₂₅, 2, 0) (dual of [(195318, 2), 390636, 1]-NRT-code) (see above)
  5. linear OOA(25⁰, 195318, F₂₅, 2, 0) (dual of [(195318, 2), 390636, 1]-NRT-code) (see above)
  6. linear OOA(25⁰, 195318, F₂₅, 2, 0) (dual of [(195318, 2), 390636, 1]-NRT-code) (see above)
  7. linear OOA(25⁰, 195318, F₂₅, 2, 0) (dual of [(195318, 2), 390636, 1]-NRT-code) (see above)
  8. linear OOA(25⁰, 195318, F₂₅, 2, 0) (dual of [(195318, 2), 390636, 1]-NRT-code) (see above)
  9. linear OOA(25⁰, 195318, F₂₅, 2, 0) (dual of [(195318, 2), 390636, 1]-NRT-code) (see above)
  10. linear OOA(25⁰, 195318, F₂₅, 2, 0) (dual of [(195318, 2), 390636, 1]-NRT-code) (see above)
  11. linear OOA(25⁰, 195318, F₂₅, 2, 0) (dual of [(195318, 2), 390636, 1]-NRT-code) (see above)
  12. linear OOA(25⁰, 195318, F₂₅, 2, 0) (dual of [(195318, 2), 390636, 1]-NRT-code) (see above)
  13. linear OOA(25⁰, 195318, F₂₅, 2, 0) (dual of [(195318, 2), 390636, 1]-NRT-code) (see above)
  14. linear OOA(25⁰, 195318, F₂₅, 2, 0) (dual of [(195318, 2), 390636, 1]-NRT-code) (see above)
  15. linear OOA(25⁰, 195318, F₂₅, 2, 0) (dual of [(195318, 2), 390636, 1]-NRT-code) (see above)
  16. linear OOA(25⁰, 195318, F₂₅, 2, 0) (dual of [(195318, 2), 390636, 1]-NRT-code) (see above)
  17. linear OOA(25⁰, 195318, F₂₅, 2, 0) (dual of [(195318, 2), 390636, 1]-NRT-code) (see above)
  18. linear OOA(25⁰, 195318, F₂₅, 2, 0) (dual of [(195318, 2), 390636, 1]-NRT-code) (see above)
  19. linear OOA(25⁰, 195318, F₂₅, 2, 0) (dual of [(195318, 2), 390636, 1]-NRT-code) (see above)
  20. linear OOA(25⁰, 195318, F₂₅, 2, 0) (dual of [(195318, 2), 390636, 1]-NRT-code) (see above)
  21. linear OOA(25¹, 195318, F₂₅, 2, 1) (dual of [(195318, 2), 390635, 2]-NRT-code), using
    - discarding factors / shortening the dual code based on linear OOA(25¹, s, F₂₅, 2, 1) for arbitrarily large s, using
      - appending 1 arbitrary column [i] based on linear OA(25¹, s, F₂₅, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
        parity-check code [i]
  22. linear OOA(25¹, 195318, F₂₅, 2, 1) (dual of [(195318, 2), 390635, 2]-NRT-code) (see above)
  23. linear OOA(25¹, 195318, F₂₅, 2, 1) (dual of [(195318, 2), 390635, 2]-NRT-code) (see above)
  24. linear OOA(25⁵, 195318, F₂₅, 2, 2) (dual of [(195318, 2), 390631, 3]-NRT-code), using
    - discarding factors / shortening the dual code based on linear OOA(25⁵, 406901, F₂₅, 2, 2) (dual of [(406901, 2), 813797, 3]-NRT-code), using
      - appending kth column [i] based on linear OA(25⁵, 406901, F₂₅, 2) (dual of [406901, 406896, 3]-code), using
        Hamming code H(5,25) [i]
  25. linear OOA(25¹⁸, 195318, F₂₅, 2, 5) (dual of [(195318, 2), 390618, 6]-NRT-code), using
    - OOA 2-folding [i] based on linear OA(25¹⁸, 390636, F₂₅, 5) (dual of [390636, 390618, 6]-code), using
      - constructionÂ X4 applied to C([0,2]) âŠ‚ C([0,1]) [i] based on
        linear OA(25¹⁷, 390626, F₂₅, 5) (dual of [390626, 390609, 6]-code), using the expurgated narrow-sense BCH-code C(I) with length 390626Â | 25⁸âˆ’1, defining interval IÂ =Â [0,2], and minimum distance dÂ â‰¥ |{−2,−1,0,1,2}|+1Â =Â 6 (BCH-bound) [i]
        linear OA(25⁹, 390626, F₂₅, 3) (dual of [390626, 390617, 4]-code or 390626-cap in PG(8,25)), using the expurgated narrow-sense BCH-code C(I) with length 390626Â | 25⁸âˆ’1, defining interval IÂ =Â [0,1], and minimum distance dÂ â‰¥ |{−1,0,1}|+1Â =Â 4 (BCH-bound) [i]
        linear OA(25⁹, 10, F₂₅, 9) (dual of [10, 1, 10]-code or 10-arc in PG(8,25)), using
        dual of repetition code with length 10 [i]
        linear OA(25¹, 10, F₂₅, 1) (dual of [10, 9, 2]-code), using
        discarding factors / shortening the dual code based on linear OA(25¹, 25, F₂₅, 1) (dual of [25, 24, 2]-code), using
        Reedâ€“Solomon code RS(24,25) [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.