MinT - Information on Result #703562

Information on Result #703562

Linear OA(3¹²⁹, 270, F₃, 41) (dual of [270, 141, 42]-code), using constructionÂ XX applied to C₁Â =Â C([82,121]), C₂Â =Â C([88,122]), C₃Â =Â C₁Â +Â C₂Â =Â C([88,121]), and C_âˆ©Â =Â C₁Â âˆ©Â C₂Â =Â C([82,122]) based on

linear OA(3¹¹⁶, 242, F₃, 40) (dual of [242, 126, 41]-code), using the primitive BCH-code C(I) with length 242Â = 3⁵âˆ’1, defining interval IÂ =Â {82,83,…,121}, and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 41 [i]
linear OA(3¹⁰⁶, 242, F₃, 35) (dual of [242, 136, 36]-code), using the primitive BCH-code C(I) with length 242Â = 3⁵âˆ’1, defining interval IÂ =Â {88,89,…,122}, and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 36 [i]
linear OA(3¹²¹, 242, F₃, 41) (dual of [242, 121, 42]-code), using the primitive BCH-code C(I) with length 242Â = 3⁵âˆ’1, defining interval IÂ =Â {82,83,…,122}, and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 42 [i]
linear OA(3¹⁰¹, 242, F₃, 34) (dual of [242, 141, 35]-code), using the primitive BCH-code C(I) with length 242Â = 3⁵âˆ’1, defining interval IÂ =Â {88,89,…,121}, and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 35 [i]
linear OA(3⁸, 23, F₃, 5) (dual of [23, 15, 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), 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(3⁰, 5, F₃, 0) (dual of [5, 5, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(3⁰, s, F₃, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
  - OA with only one run / dual of code without redundancy [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(3¹²⁹, 135, F₃, 2, 41) (dual of [(135, 2), 141, 42]-NRT-code)	[i]		OOA Folding
2	Linear OOA(3¹²⁹, 90, F₃, 3, 41) (dual of [(90, 3), 141, 42]-NRT-code)	[i]		OOA Folding