MinT - Information on Result #703493

Information on Result #703493

Linear OA(3¹²⁷, 288, F₃, 37) (dual of [288, 161, 38]-code), using constructionÂ XX applied to C₁Â =Â C([236,24]), C₂Â =Â C([0,30]), C₃Â =Â C₁Â +Â C₂Â =Â C([0,24]), and C_âˆ©Â =Â C₁Â âˆ©Â C₂Â =Â C([236,30]) based on

linear OA(3¹⁰¹, 242, F₃, 31) (dual of [242, 141, 32]-code), using the primitive BCH-code C(I) with length 242Â = 3⁵âˆ’1, defining interval IÂ =Â {−6,−5,…,24}, and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 32 [i]
linear OA(3⁹¹, 242, F₃, 31) (dual of [242, 151, 32]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 242Â = 3⁵âˆ’1, defining interval IÂ =Â [0,30], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 32 [i]
linear OA(3¹¹¹, 242, F₃, 37) (dual of [242, 131, 38]-code), using the primitive BCH-code C(I) with length 242Â = 3⁵âˆ’1, defining interval IÂ =Â {−6,−5,…,30}, and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 38 [i]
linear OA(3⁸¹, 242, F₃, 25) (dual of [242, 161, 26]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 242Â = 3⁵âˆ’1, defining interval IÂ =Â [0,24], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 26 [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(3⁸, 18, F₃, 5) (dual of [18, 10, 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) (see above)
    2. nonexistence of linear OA(3¹⁷, 21, F₃, 12) (dual of [21, 4, 13]-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		Method
1	Linear OA(3¹²⁸, 289, F₃, 37) (dual of [289, 161, 38]-code)	[i]	Code Embedding in Larger Space
2	Linear OA(3¹²⁹, 290, F₃, 37) (dual of [290, 161, 38]-code)	[i]	Code Embedding in Larger Space
3	Linear OA(3¹²⁶, 287, F₃, 36) (dual of [287, 161, 37]-code)	[i]	Truncation
4	Linear OOA(3¹²⁷, 144, F₃, 2, 37) (dual of [(144, 2), 161, 38]-NRT-code)	[i]	OOA Folding