MinT - Information on Result #705650

Information on Result #705650

Linear OA(3²²², 763, F₃, 55) (dual of [763, 541, 56]-code), using constructionÂ XX applied to C₁Â =Â C([340,391]), C₂Â =Â C([337,385]), C₃Â =Â C₁Â +Â C₂Â =Â C([340,385]), and C_âˆ©Â =Â C₁Â âˆ©Â C₂Â =Â C([337,391]) based on

linear OA(3²⁰⁵, 728, F₃, 52) (dual of [728, 523, 53]-code), using the primitive BCH-code C(I) with length 728Â = 3⁶âˆ’1, defining interval IÂ =Â {340,341,…,391}, and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 53 [i]
linear OA(3¹⁹³, 728, F₃, 49) (dual of [728, 535, 50]-code), using the primitive BCH-code C(I) with length 728Â = 3⁶âˆ’1, defining interval IÂ =Â {337,338,…,385}, and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 50 [i]
linear OA(3²¹¹, 728, F₃, 55) (dual of [728, 517, 56]-code), using the primitive BCH-code C(I) with length 728Â = 3⁶âˆ’1, defining interval IÂ =Â {337,338,…,391}, and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 56 [i]
linear OA(3¹⁸¹, 728, F₃, 46) (dual of [728, 547, 47]-code), using the primitive BCH-code C(I) with length 728Â = 3⁶âˆ’1, defining interval IÂ =Â {340,341,…,385}, and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 47 [i]
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]
linear OA(3³, 9, F₃, 2) (dual of [9, 6, 3]-code), using
- discarding factors / shortening the dual code based on linear OA(3³, 13, F₃, 2) (dual of [13, 10, 3]-code), using
  - Hamming code H(3,3) [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		Method
1	Linear OOA(3²²², 381, F₃, 2, 55) (dual of [(381, 2), 540, 56]-NRT-code)	[i]	OOA Folding
2	Linear OOA(3²²², 254, F₃, 3, 55) (dual of [(254, 3), 540, 56]-NRT-code)	[i]
3	Linear OOA(3²²², 190, F₃, 4, 55) (dual of [(190, 4), 538, 56]-NRT-code)	[i]