MinT - Information on Result #818321

Information on Result #818321

Linear OOA(3²²⁵, 377, F₃, 2, 57) (dual of [(377, 2), 529, 58]-NRT-code), using OOA 2-folding based on linear OA(3²²⁵, 754, F₃, 57) (dual of [754, 529, 58]-code), using

constructionÂ XX applied to C₁Â =Â C([337,392]), C₂Â =Â C([336,386]), C₃Â =Â C₁Â +Â C₂Â =Â C([337,386]), and C_âˆ©Â =Â C₁Â âˆ©Â C₂Â =Â C([336,392]) [i] based on
1. linear OA(3²¹⁴, 728, F₃, 56) (dual of [728, 514, 57]-code), using the primitive BCH-code C(I) with length 728Â = 3⁶âˆ’1, defining interval IÂ =Â {337,338,…,392}, and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 57 [i]
2. linear OA(3²⁰², 728, F₃, 51) (dual of [728, 526, 52]-code), using the primitive BCH-code C(I) with length 728Â = 3⁶âˆ’1, defining interval IÂ =Â {336,337,…,386}, and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 52 [i]
3. linear OA(3²¹⁷, 728, F₃, 57) (dual of [728, 511, 58]-code), using the primitive BCH-code C(I) with length 728Â = 3⁶âˆ’1, defining interval IÂ =Â {336,337,…,392}, and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 58 [i]
4. linear OA(3¹⁹⁹, 728, F₃, 50) (dual of [728, 529, 51]-code), using the primitive BCH-code C(I) with length 728Â = 3⁶âˆ’1, defining interval IÂ =Â {337,338,…,386}, and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 51 [i]
5. linear OA(3⁸, 23, F₃, 5) (dual of [23, 15, 6]-code), using
  - discarding factors / shortening the dual code based on linear OA(3⁸, 26, F₃, 5) (dual of [26, 18, 6]-code), using
    - dual code (with bound on d by constructionÂ Y1) [i] based on
      1. linear OA(3¹⁸, 26, F₃, 12) (dual of [26, 8, 13]-code), using
        2 times truncation [i] based on linear OA(3²⁰, 28, F₃, 14) (dual of [28, 8, 15]-code), using
        contraction [i] based on linear OA(3⁴⁸, 56, F₃, 29) (dual of [56, 8, 30]-code), using the BCH-code C(I) with length 56Â | 3⁶âˆ’1, defining interval IÂ =Â {0,1,…,28}, and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 30 [i]
      2. nonexistence of linear OA(3¹⁷, 21, F₃, 12) (dual of [21, 4, 13]-code), because
        â€œHNâ€ bound on codes from Brouwerâ€™s database [i]
6. linear OA(3⁰, 3, F₃, 0) (dual of [3, 3, 1]-code), using
  - discarding factors / shortening the dual code based on linear OA(3⁰, s, F₃, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
    - OA with only one run / dual of code without redundancy [i]

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(3²²⁷, 378, F₃, 2, 57) (dual of [(378, 2), 529, 58]-NRT-code)	[i]		NRT-Code Embedding in Larger Space
2	Linear OOA(3²²⁶, 377, F₃, 2, 57) (dual of [(377, 2), 528, 58]-NRT-code)	[i]		OOA Duplication