MinT - Information on Result #1197469

Information on Result #1197469

Linear OOA(27⁵³, 2102091, F₂₇, 10, 9) (dual of [(2102091, 10), 21020857, 10]-NRT-code), using OOA 2-folding and stacking with additional row based on linear OOA(27⁵³, 4204183, F₂₇, 2, 9) (dual of [(4204183, 2), 8408313, 10]-NRT-code), using

(u,Â u+v)-construction [i] based on
1. linear OOA(27¹², 9882, F₂₇, 2, 4) (dual of [(9882, 2), 19752, 5]-NRT-code), using
  - OOA 2-folding [i] based on linear OA(27¹², 19764, F₂₇, 4) (dual of [19764, 19752, 5]-code), using
    - generalized (u,Â u+v)-construction [i] based on
      1. linear OA(27⁰, 732, F₂₇, 0) (dual of [732, 732, 1]-code), using
        discarding factors / shortening the dual code based on linear OA(27⁰, s, F₂₇, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
        OA with only one run / dual of code without redundancy [i]
      2. linear OA(27⁰, 732, F₂₇, 0) (dual of [732, 732, 1]-code) (see above)
      3. linear OA(27⁰, 732, F₂₇, 0) (dual of [732, 732, 1]-code) (see above)
      4. linear OA(27⁰, 732, F₂₇, 0) (dual of [732, 732, 1]-code) (see above)
      5. linear OA(27⁰, 732, F₂₇, 0) (dual of [732, 732, 1]-code) (see above)
      6. linear OA(27⁰, 732, F₂₇, 0) (dual of [732, 732, 1]-code) (see above)
      7. linear OA(27⁰, 732, F₂₇, 0) (dual of [732, 732, 1]-code) (see above)
      8. linear OA(27⁰, 732, F₂₇, 0) (dual of [732, 732, 1]-code) (see above)
      9. linear OA(27⁰, 732, F₂₇, 0) (dual of [732, 732, 1]-code) (see above)
      10. linear OA(27⁰, 732, F₂₇, 0) (dual of [732, 732, 1]-code) (see above)
      11. linear OA(27⁰, 732, F₂₇, 0) (dual of [732, 732, 1]-code) (see above)
      12. linear OA(27⁰, 732, F₂₇, 0) (dual of [732, 732, 1]-code) (see above)
      13. linear OA(27⁰, 732, F₂₇, 0) (dual of [732, 732, 1]-code) (see above)
      14. linear OA(27⁰, 732, F₂₇, 0) (dual of [732, 732, 1]-code) (see above)
      15. linear OA(27⁰, 732, F₂₇, 0) (dual of [732, 732, 1]-code) (see above)
      16. linear OA(27⁰, 732, F₂₇, 0) (dual of [732, 732, 1]-code) (see above)
      17. linear OA(27⁰, 732, F₂₇, 0) (dual of [732, 732, 1]-code) (see above)
      18. linear OA(27⁰, 732, F₂₇, 0) (dual of [732, 732, 1]-code) (see above)
      19. linear OA(27⁰, 732, F₂₇, 0) (dual of [732, 732, 1]-code) (see above)
      20. linear OA(27⁰, 732, F₂₇, 0) (dual of [732, 732, 1]-code) (see above)
      21. linear OA(27⁰, 732, F₂₇, 0) (dual of [732, 732, 1]-code) (see above)
      22. linear OA(27⁰, 732, F₂₇, 0) (dual of [732, 732, 1]-code) (see above)
      23. linear OA(27⁰, 732, F₂₇, 0) (dual of [732, 732, 1]-code) (see above)
      24. linear OA(27¹, 732, F₂₇, 1) (dual of [732, 731, 2]-code), using
        discarding factors / shortening the dual code based on linear OA(27¹, s, F₂₇, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
        parity-check code [i]
      25. linear OA(27¹, 732, F₂₇, 1) (dual of [732, 731, 2]-code) (see above)
      26. linear OA(27³, 732, F₂₇, 2) (dual of [732, 729, 3]-code), using
        discarding factors / shortening the dual code based on linear OA(27³, 757, F₂₇, 2) (dual of [757, 754, 3]-code), using
        Hamming code H(3,27) [i]
      27. linear OA(27⁷, 732, F₂₇, 4) (dual of [732, 725, 5]-code), using
        constructionÂ XX applied to C₁Â =Â C([727,1]), C₂Â =Â C([0,2]), C₃Â =Â C₁Â +Â C₂Â =Â C([0,1]), and C_âˆ©Â =Â C₁Â âˆ©Â C₂Â =Â C([727,2]) [i] based on
        linear OA(27⁵, 728, F₂₇, 3) (dual of [728, 723, 4]-code or 728-cap in PG(4,27)), using the primitive BCH-code C(I) with length 728Â = 27²âˆ’1, defining interval IÂ =Â {−1,0,1}, and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 4 [i]
        linear OA(27⁵, 728, F₂₇, 3) (dual of [728, 723, 4]-code or 728-cap in PG(4,27)), using the primitive expurgated narrow-sense BCH-code C(I) with length 728Â = 27²âˆ’1, defining interval IÂ =Â [0,2], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 4 [i]
        linear OA(27⁷, 728, F₂₇, 4) (dual of [728, 721, 5]-code), using the primitive BCH-code C(I) with length 728Â = 27²âˆ’1, defining interval IÂ =Â {−1,0,1,2}, and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 5 [i]
        linear OA(27³, 728, F₂₇, 2) (dual of [728, 725, 3]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 728Â = 27²âˆ’1, defining interval IÂ =Â [0,1], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 3 [i]
        linear OA(27⁰, 2, F₂₇, 0) (dual of [2, 2, 1]-code), using
        discarding factors / shortening the dual code based on linear OA(27⁰, s, F₂₇, 0) (dual of [s, s, 1]-code) for arbitrarily large s (see above)
        linear OA(27⁰, 2, F₂₇, 0) (dual of [2, 2, 1]-code) (see above)
2. linear OOA(27⁴¹, 4194301, F₂₇, 2, 9) (dual of [(4194301, 2), 8388561, 10]-NRT-code), using
  - OOA 2-folding [i] based on linear OA(27⁴¹, 8388602, F₂₇, 9) (dual of [8388602, 8388561, 10]-code), using
    - discarding factors / shortening the dual code based on linear OA(27⁴¹, large, F₂₇, 9) (dual of [large, large−41, 10]-code), using
      - the expurgated narrow-sense BCH-code C(I) with length 14348908Â | 27¹⁰âˆ’1, defining interval IÂ =Â [0,4], and minimum distance dÂ â‰¥ |{−4,−3,…,4}|+1Â =Â 10 (BCH-bound) [i]

Mode: Constructive and linear.

Results with these parameters are outside the parameter range considered by MinT and show only up in construction trees.

Other Results with Identical Parameters

None.

Depending Results

The following results depend on this result:

	Result		This result only	Method
1	Digital (44, 53, 2102091)-net over F₂₇	[i]		Net Defined by OOA