MinT - Information on Result #869043

Information on Result #869043

Linear OOA(32¹⁵, 16432, F₃₂, 2, 5) (dual of [(16432, 2), 32849, 6]-NRT-code), using OOA 2-folding based on linear OA(32¹⁵, 32864, F₃₂, 5) (dual of [32864, 32849, 6]-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(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]
29. linear OA(32¹, 1027, F₃₂, 1) (dual of [1027, 1026, 2]-code) (see above)
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(32⁹, 1027, F₃₂, 5) (dual of [1027, 1018, 6]-code), using
  - constructionÂ XX applied to C₁Â =Â C([1022,2]), C₂Â =Â C([0,3]), C₃Â =Â C₁Â +Â C₂Â =Â C([0,2]), and C_âˆ©Â =Â C₁Â âˆ©Â C₂Â =Â C([1022,3]) [i] based on
    1. 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]
    2. linear OA(32⁷, 1023, F₃₂, 4) (dual of [1023, 1016, 5]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 1023Â = 32²âˆ’1, defining interval IÂ =Â [0,3], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 5 [i]
    3. linear OA(32⁹, 1023, F₃₂, 5) (dual of [1023, 1014, 6]-code), using the primitive BCH-code C(I) with length 1023Â = 32²âˆ’1, defining interval IÂ =Â {−1,0,1,2,3}, and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 6 [i]
    4. 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]
    5. 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)
    6. linear OA(32⁰, 2, F₃₂, 0) (dual of [2, 2, 1]-code) (see above)

Mode: Constructive and linear.

Optimality

Show details for fixed k and m, n and k, k and s, k and t, n and m, m and s, m and t, n and s, n 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(32⁶¹, 4210733, F₃₂, 2, 10) (dual of [(4210733, 2), 8421405, 11]-NRT-code)	[i]		(u,Â u+v)-Construction for OOAs
2	Linear OOA(32⁶⁶, 4210733, F₃₂, 2, 11) (dual of [(4210733, 2), 8421400, 12]-NRT-code)	[i]		(u,Â u+v)-Construction for OOAs