MinT - Information on Result #677617

Information on Result #677617

Linear OA(3⁸², 98, F₃, 46) (dual of [98, 16, 47]-code), using constructionÂ XX applied to C([1,99]) âŠ‚ C([1,81]) âŠ‚ C([1,79]) based on

linear OA(3⁷³, 80, F₃, 49) (dual of [80, 7, 50]-code), using contraction [i] based on linear OA(3¹⁵³, 160, F₃, 99) (dual of [160, 7, 100]-code), using the narrow-sense BCH-code C(I) with length 160Â | 3⁸âˆ’1, defining interval IÂ =Â [1,99], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 100 [i]
linear OA(3⁶⁵, 80, F₃, 40) (dual of [80, 15, 41]-code), using contraction [i] based on linear OA(3¹⁴⁵, 160, F₃, 81) (dual of [160, 15, 82]-code), using the narrow-sense BCH-code C(I) with length 160Â | 3⁸âˆ’1, defining interval IÂ =Â [1,81], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 82 [i]
linear OA(3⁶⁴, 80, F₃, 39) (dual of [80, 16, 40]-code), using contraction [i] based on linear OA(3¹⁴⁴, 160, F₃, 79) (dual of [160, 16, 80]-code), using the narrow-sense BCH-code C(I) with length 160Â | 3⁸âˆ’1, defining interval IÂ =Â [1,79], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 80 [i]
linear OA(3⁸, 17, F₃, 5) (dual of [17, 9, 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, 1, F₃, 0) (dual of [1, 1, 1]-code), using
- dual of repetition code with length 1 [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.

Compare with Markus Grassl’s online database of code parameters.

Other Results with Identical Parameters

None.

Depending Results

The following results depend on this result:

	Result		Method
1	Linear OA(3⁸², 98, F₃, 45) (dual of [98, 16, 46]-code)	[i]	Strength Reduction
2	Linear OA(3⁸², 98, F₃, 44) (dual of [98, 16, 45]-code)	[i]
3	Linear OA(3⁸², 98, F₃, 43) (dual of [98, 16, 44]-code)	[i]
4	Linear OA(3⁸², 98, F₃, 42) (dual of [98, 16, 43]-code)	[i]