MinT - Information on Result #705679

Information on Result #705679

Linear OA(3²⁴¹, 790, F₃, 57) (dual of [790, 549, 58]-code), using constructionÂ XX applied to C₁Â =Â C([342,392]), C₂Â =Â C([336,385]), C₃Â =Â C₁Â +Â C₂Â =Â C([342,385]), and C_âˆ©Â =Â C₁Â âˆ©Â C₂Â =Â C([336,392]) based on

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 {342,343,…,392}, and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 52 [i]
linear OA(3¹⁹⁶, 728, F₃, 50) (dual of [728, 532, 51]-code), using the primitive BCH-code C(I) with length 728Â = 3⁶âˆ’1, defining interval IÂ =Â {336,337,…,385}, and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 51 [i]
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]
linear OA(3¹⁷⁵, 728, F₃, 44) (dual of [728, 553, 45]-code), using the primitive BCH-code C(I) with length 728Â = 3⁶âˆ’1, defining interval IÂ =Â {342,343,…,385}, and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 45 [i]
linear OA(3¹⁴, 37, F₃, 6) (dual of [37, 23, 7]-code), using
- discarding factors / shortening the dual code based on linear OA(3¹⁴, 53, F₃, 6) (dual of [53, 39, 7]-code), using
  - codes constructed by inverting constructionÂ Y₁ [i]
linear OA(3⁸, 25, F₃, 5) (dual of [25, 17, 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]

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(3²⁴¹, 395, F₃, 2, 57) (dual of [(395, 2), 549, 58]-NRT-code)	[i]		OOA Folding
2	Linear OOA(3²⁴¹, 263, F₃, 3, 57) (dual of [(263, 3), 548, 58]-NRT-code)	[i]		OOA Folding