MinT - Information on Result #703536

Information on Result #703536

Linear OA(3¹²⁴, 270, F₃, 39) (dual of [270, 146, 40]-code), using constructionÂ XX applied to C₁Â =Â C([84,121]), C₂Â =Â C([90,122]), C₃Â =Â C₁Â +Â C₂Â =Â C([90,121]), and C_âˆ©Â =Â C₁Â âˆ©Â C₂Â =Â C([84,122]) based on

linear OA(3¹¹¹, 242, F₃, 38) (dual of [242, 131, 39]-code), using the primitive BCH-code C(I) with length 242Â = 3⁵âˆ’1, defining interval IÂ =Â {84,85,…,121}, and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 39 [i]
linear OA(3¹⁰¹, 242, F₃, 33) (dual of [242, 141, 34]-code), using the primitive BCH-code C(I) with length 242Â = 3⁵âˆ’1, defining interval IÂ =Â {90,91,…,122}, and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 34 [i]
linear OA(3¹¹⁶, 242, F₃, 39) (dual of [242, 126, 40]-code), using the primitive BCH-code C(I) with length 242Â = 3⁵âˆ’1, defining interval IÂ =Â {84,85,…,122}, and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 40 [i]
linear OA(3⁹⁶, 242, F₃, 32) (dual of [242, 146, 33]-code), using the primitive BCH-code C(I) with length 242Â = 3⁵âˆ’1, defining interval IÂ =Â {90,91,…,121}, and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 33 [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(3¹²⁴, 135, F₃, 2, 39) (dual of [(135, 2), 146, 40]-NRT-code)	[i]		OOA Folding
2	Linear OOA(3¹²⁴, 90, F₃, 3, 39) (dual of [(90, 3), 146, 40]-NRT-code)	[i]		OOA Folding