MinT - Information on Result #704576

Information on Result #704576

Linear OA(3¹³³, 764, F₃, 32) (dual of [764, 631, 33]-code), using constructionÂ XX applied to C₁Â =Â C([334,363]), C₂Â =Â C([340,365]), C₃Â =Â C₁Â +Â C₂Â =Â C([340,363]), and C_âˆ©Â =Â C₁Â âˆ©Â C₂Â =Â C([334,365]) based on

linear OA(3¹¹⁷, 728, F₃, 30) (dual of [728, 611, 31]-code), using the primitive BCH-code C(I) with length 728Â = 3⁶âˆ’1, defining interval IÂ =Â {334,335,…,363}, and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 31 [i]
linear OA(3¹⁰³, 728, F₃, 26) (dual of [728, 625, 27]-code), using the primitive BCH-code C(I) with length 728Â = 3⁶âˆ’1, defining interval IÂ =Â {340,341,…,365}, and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 27 [i]
linear OA(3¹²⁴, 728, F₃, 32) (dual of [728, 604, 33]-code), using the primitive BCH-code C(I) with length 728Â = 3⁶âˆ’1, defining interval IÂ =Â {334,335,…,365}, and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 33 [i]
linear OA(3⁹⁶, 728, F₃, 24) (dual of [728, 632, 25]-code), using the primitive BCH-code C(I) with length 728Â = 3⁶âˆ’1, defining interval IÂ =Â {340,341,…,363}, and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 25 [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(3¹, 8, F₃, 1) (dual of [8, 7, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(3¹, s, F₃, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
  - parity-check code [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(3¹³³, 731, F₃, 2, 32) (dual of [(731, 2), 1329, 33]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
2	Linear OOA(3¹³³, 731, F₃, 3, 32) (dual of [(731, 3), 2060, 33]-NRT-code)	[i]
3	Linear OOA(3¹³³, 731, F₃, 4, 32) (dual of [(731, 4), 2791, 33]-NRT-code)	[i]
4	Linear OOA(3¹³³, 731, F₃, 5, 32) (dual of [(731, 5), 3522, 33]-NRT-code)	[i]
5	Digital (101, 133, 731)-net over F₃	[i]
6	Linear OOA(3¹³³, 382, F₃, 2, 32) (dual of [(382, 2), 631, 33]-NRT-code)	[i]	OOA Folding