MinT - Information on Result #705477

Information on Result #705477

Linear OA(3²¹⁷, 781, F₃, 52) (dual of [781, 564, 53]-code), using constructionÂ XX applied to C₁Â =Â C([722,40]), C₂Â =Â C([0,45]), C₃Â =Â C₁Â +Â C₂Â =Â C([0,40]), and C_âˆ©Â =Â C₁Â âˆ©Â C₂Â =Â C([722,45]) based on

linear OA(3¹⁸⁴, 728, F₃, 47) (dual of [728, 544, 48]-code), using the primitive BCH-code C(I) with length 728Â = 3⁶âˆ’1, defining interval IÂ =Â {−6,−5,…,40}, and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 48 [i]
linear OA(3¹⁷⁸, 728, F₃, 46) (dual of [728, 550, 47]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 728Â = 3⁶âˆ’1, defining interval IÂ =Â [0,45], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 47 [i]
linear OA(3²⁰², 728, F₃, 52) (dual of [728, 526, 53]-code), using the primitive BCH-code C(I) with length 728Â = 3⁶âˆ’1, defining interval IÂ =Â {−6,−5,…,45}, and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 53 [i]
linear OA(3¹⁶⁰, 728, F₃, 41) (dual of [728, 568, 42]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 728Â = 3⁶âˆ’1, defining interval IÂ =Â [0,40], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 42 [i]
linear OA(3⁸, 28, F₃, 5) (dual of [28, 20, 6]-code), using
- dual code (with bound on d by constructionÂ Y1) [i] based on
  1. 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(3¹⁹, 23, F₃, 14) (dual of [23, 4, 15]-code), because
    - 2 times truncation [i] would yield linear OA(3¹⁷, 21, F₃, 12) (dual of [21, 4, 13]-code), but
      - â€œHNâ€ bound on codes from Brouwerâ€™s database [i]
linear OA(3⁷, 25, F₃, 4) (dual of [25, 18, 5]-code), using
- discarding factors / shortening the dual code based on linear OA(3⁷, 26, F₃, 4) (dual of [26, 19, 5]-code), using
  - the primitive expurgated narrow-sense BCH-code C(I) with length 26Â = 3³âˆ’1, defining interval IÂ =Â [0,2], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 5 [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 OA(3²¹⁸, 782, F₃, 52) (dual of [782, 564, 53]-code)	[i]	Code Embedding in Larger Space
2	Linear OOA(3²¹⁷, 390, F₃, 2, 52) (dual of [(390, 2), 563, 53]-NRT-code)	[i]	OOA Folding
3	Linear OOA(3²¹⁷, 260, F₃, 3, 52) (dual of [(260, 3), 563, 53]-NRT-code)	[i]	OOA Folding