MinT - Information on Result #901854

Information on Result #901854

Linear OOA(32⁵³, 4210733, F₃₂, 2, 9) (dual of [(4210733, 2), 8421413, 10]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(32¹², 16432, F₃₂, 2, 4) (dual of [(16432, 2), 32852, 5]-NRT-code), using
- OOA 2-folding [i] based on linear OA(32¹², 32864, F₃₂, 4) (dual of [32864, 32852, 5]-code), using
  - generalized (u,Â u+v)-construction [i] based on
    1. linear OA(32⁰, 1027, F₃₂, 0) (dual of [1027, 1027, 1]-code), using
      - discarding factors / shortening the dual code based on linear OA(32⁰, s, F₃₂, 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(32⁰, 1027, F₃₂, 0) (dual of [1027, 1027, 1]-code) (see above)
    3. linear OA(32⁰, 1027, F₃₂, 0) (dual of [1027, 1027, 1]-code) (see above)
    4. linear OA(32⁰, 1027, F₃₂, 0) (dual of [1027, 1027, 1]-code) (see above)
    5. linear OA(32⁰, 1027, F₃₂, 0) (dual of [1027, 1027, 1]-code) (see above)
    6. linear OA(32⁰, 1027, F₃₂, 0) (dual of [1027, 1027, 1]-code) (see above)
    7. linear OA(32⁰, 1027, F₃₂, 0) (dual of [1027, 1027, 1]-code) (see above)
    8. linear OA(32⁰, 1027, F₃₂, 0) (dual of [1027, 1027, 1]-code) (see above)
    9. linear OA(32⁰, 1027, F₃₂, 0) (dual of [1027, 1027, 1]-code) (see above)
    10. linear OA(32⁰, 1027, F₃₂, 0) (dual of [1027, 1027, 1]-code) (see above)
    11. linear OA(32⁰, 1027, F₃₂, 0) (dual of [1027, 1027, 1]-code) (see above)
    12. linear OA(32⁰, 1027, F₃₂, 0) (dual of [1027, 1027, 1]-code) (see above)
    13. linear OA(32⁰, 1027, F₃₂, 0) (dual of [1027, 1027, 1]-code) (see above)
    14. linear OA(32⁰, 1027, F₃₂, 0) (dual of [1027, 1027, 1]-code) (see above)
    15. linear OA(32⁰, 1027, F₃₂, 0) (dual of [1027, 1027, 1]-code) (see above)
    16. linear OA(32⁰, 1027, F₃₂, 0) (dual of [1027, 1027, 1]-code) (see above)
    17. linear OA(32⁰, 1027, F₃₂, 0) (dual of [1027, 1027, 1]-code) (see above)
    18. linear OA(32⁰, 1027, F₃₂, 0) (dual of [1027, 1027, 1]-code) (see above)
    19. linear OA(32⁰, 1027, F₃₂, 0) (dual of [1027, 1027, 1]-code) (see above)
    20. linear OA(32⁰, 1027, F₃₂, 0) (dual of [1027, 1027, 1]-code) (see above)
    21. linear OA(32⁰, 1027, F₃₂, 0) (dual of [1027, 1027, 1]-code) (see above)
    22. linear OA(32⁰, 1027, F₃₂, 0) (dual of [1027, 1027, 1]-code) (see above)
    23. linear OA(32⁰, 1027, F₃₂, 0) (dual of [1027, 1027, 1]-code) (see above)
    24. linear OA(32⁰, 1027, F₃₂, 0) (dual of [1027, 1027, 1]-code) (see above)
    25. linear OA(32⁰, 1027, F₃₂, 0) (dual of [1027, 1027, 1]-code) (see above)
    26. linear OA(32⁰, 1027, F₃₂, 0) (dual of [1027, 1027, 1]-code) (see above)
    27. linear OA(32⁰, 1027, F₃₂, 0) (dual of [1027, 1027, 1]-code) (see above)
    28. linear OA(32⁰, 1027, F₃₂, 0) (dual of [1027, 1027, 1]-code) (see above)
    29. linear OA(32¹, 1027, F₃₂, 1) (dual of [1027, 1026, 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]
    30. linear OA(32¹, 1027, F₃₂, 1) (dual of [1027, 1026, 2]-code) (see above)
    31. linear OA(32³, 1027, F₃₂, 2) (dual of [1027, 1024, 3]-code), using
      - discarding factors / shortening the dual code based on linear OA(32³, 1057, F₃₂, 2) (dual of [1057, 1054, 3]-code), using
        Hamming code H(3,32) [i]
    32. linear OA(32⁷, 1027, F₃₂, 4) (dual of [1027, 1020, 5]-code), using
      - constructionÂ XX applied to C₁Â =Â C([1022,1]), 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([1022,2]) [i] based on
        linear OA(32⁵, 1023, F₃₂, 3) (dual of [1023, 1018, 4]-code or 1023-cap in PG(4,32)), using the primitive BCH-code C(I) with length 1023Â = 32²âˆ’1, defining interval IÂ =Â {−1,0,1}, and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 4 [i]
        linear OA(32⁵, 1023, F₃₂, 3) (dual of [1023, 1018, 4]-code or 1023-cap in PG(4,32)), using the primitive expurgated narrow-sense BCH-code C(I) with length 1023Â = 32²âˆ’1, defining interval IÂ =Â [0,2], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 4 [i]
        linear OA(32⁷, 1023, F₃₂, 4) (dual of [1023, 1016, 5]-code), using the primitive BCH-code C(I) with length 1023Â = 32²âˆ’1, defining interval IÂ =Â {−1,0,1,2}, and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 5 [i]
        linear OA(32³, 1023, F₃₂, 2) (dual of [1023, 1020, 3]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 1023Â = 32²âˆ’1, defining interval IÂ =Â [0,1], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 3 [i]
        linear OA(32⁰, 2, F₃₂, 0) (dual of [2, 2, 1]-code), using
        discarding factors / shortening the dual code based on linear OA(32⁰, s, F₃₂, 0) (dual of [s, s, 1]-code) for arbitrarily large s (see above)
        linear OA(32⁰, 2, F₃₂, 0) (dual of [2, 2, 1]-code) (see above)
linear OOA(32⁴¹, 4194301, F₃₂, 2, 9) (dual of [(4194301, 2), 8388561, 10]-NRT-code), using
- OOA 2-folding [i] based on linear OA(32⁴¹, 8388602, F₃₂, 9) (dual of [8388602, 8388561, 10]-code), using
  - discarding factors / shortening the dual code based on linear OA(32⁴¹, large, F₃₂, 9) (dual of [large, large−41, 10]-code), using
    - the expurgated narrow-sense BCH-code C(I) with length 33554433Â | 32¹⁰âˆ’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.

Optimality

Show details for fixed k and m, k and s, k and t, m and s, m and t.

Other Results with Identical Parameters

None.

Depending Results

The following results depend on this result:

	Result		This result only	Method
1	Linear OOA(32⁵³, 2105366, F₃₂, 10, 9) (dual of [(2105366, 10), 21053607, 10]-NRT-code)	[i]		OOA Folding and Stacking with Additional Row