MinT - Information on Result #704625

Information on Result #704625

Linear OA(3¹⁴⁹, 788, F₃, 33) (dual of [788, 639, 34]-code), using constructionÂ XX applied to C₁Â =Â C([722,21]), C₂Â =Â C([0,27]), C₃Â =Â C₁Â +Â C₂Â =Â C([0,21]), and C_âˆ©Â =Â C₁Â âˆ©Â C₂Â =Â C([722,27]) based on

linear OA(3¹⁰⁹, 728, F₃, 28) (dual of [728, 619, 29]-code), using the primitive BCH-code C(I) with length 728Â = 3⁶âˆ’1, defining interval IÂ =Â {−6,−5,…,21}, and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 29 [i]
linear OA(3¹⁰⁹, 728, F₃, 28) (dual of [728, 619, 29]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 728Â = 3⁶âˆ’1, defining interval IÂ =Â [0,27], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 29 [i]
linear OA(3¹³³, 728, F₃, 34) (dual of [728, 595, 35]-code), using the primitive BCH-code C(I) with length 728Â = 3⁶âˆ’1, defining interval IÂ =Â {−6,−5,…,27}, and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 35 [i]
linear OA(3⁸⁵, 728, F₃, 22) (dual of [728, 643, 23]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 728Â = 3⁶âˆ’1, defining interval IÂ =Â [0,21], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 23 [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, 32, F₃, 4) (dual of [32, 24, 5]-code), using
- discarding factors / shortening the dual code based on linear OA(3⁸, 41, F₃, 4) (dual of [41, 33, 5]-code), using
  - the narrow-sense BCH-code C(I) with length 41Â | 3⁸âˆ’1, defining interval IÂ =Â [1,1], and minimum distance dÂ â‰¥ |{−3,−1,1,3}|+1Â =Â 5 (BCH-bound) [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(3¹⁴⁹, 394, F₃, 2, 33) (dual of [(394, 2), 639, 34]-NRT-code)	[i]		OOA Folding