MinT - Information on Result #2268267

Information on Result #2268267

Linear OA(3¹⁵², 165, F₃, 86) (dual of [165, 13, 87]-code), using 1 times code embedding in larger space based on linear OA(3¹⁵¹, 164, F₃, 86) (dual of [164, 13, 87]-code), using

juxtaposition [i] based on
1. linear OA(3⁶⁶, 79, F₃, 41) (dual of [79, 13, 42]-code), using
  - discarding factors / shortening the dual code based on linear OA(3⁶⁶, 80, F₃, 41) (dual of [80, 14, 42]-code), using
    - the primitive expurgated narrow-sense BCH-code C(I) with length 80Â = 3⁴âˆ’1, defining interval IÂ =Â [0,40], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 42 [i]
2. linear OA(3⁷², 85, F₃, 44) (dual of [85, 13, 45]-code), using
  - constructionÂ XX applied to C₁Â =Â C([0,81]), C₂Â =Â C([1,87]), C₃Â =Â C₁Â +Â C₂Â =Â C([1,81]), and C_âˆ©Â =Â C₁Â âˆ©Â C₂Â =Â C([0,87]) [i] based on
    1. linear OA(3⁶⁶, 80, F₃, 41) (dual of [80, 14, 42]-code), using contraction [i] based on linear OA(3¹⁴⁶, 160, F₃, 83) (dual of [160, 14, 84]-code), using the expurgated narrow-sense BCH-code C(I) with length 160Â | 3⁸âˆ’1, defining interval IÂ =Â [0,81], and minimum distance dÂ â‰¥ |{−1,0,…,81}|+1Â =Â 84 (BCH-bound) [i]
    2. linear OA(3⁶⁹, 80, F₃, 43) (dual of [80, 11, 44]-code), using contraction [i] based on linear OA(3¹⁴⁹, 160, F₃, 87) (dual of [160, 11, 88]-code), using the narrow-sense BCH-code C(I) with length 160Â | 3⁸âˆ’1, defining interval IÂ =Â [1,87], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 88 [i]
    3. linear OA(3⁷⁰, 80, F₃, 44) (dual of [80, 10, 45]-code), using contraction [i] based on linear OA(3¹⁵⁰, 160, F₃, 89) (dual of [160, 10, 90]-code), using the expurgated narrow-sense BCH-code C(I) with length 160Â | 3⁸âˆ’1, defining interval IÂ =Â [0,87], and minimum distance dÂ â‰¥ |{−1,0,…,87}|+1Â =Â 90 (BCH-bound) [i]
    4. 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]
    5. linear OA(3⁰, 1, F₃, 0) (dual of [1, 1, 1]-code), using
      - dual of repetition code with length 1 [i]
    6. linear OA(3², 4, F₃, 2) (dual of [4, 2, 3]-code or 4-arc in PG(1,3)), using
      - extended Reedâ€“Solomon code RS_e(2,3) [i]
      - Hamming code H(2,3) [i]
      - Simplex code S(2,3) [i]
      - the Tetracode [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		This result only	Method
1	Linear OOA(3¹⁵², 55, F₃, 3, 86) (dual of [(55, 3), 13, 87]-NRT-code)	[i]		OOA Folding
2	Linear OOA(3¹⁵², 33, F₃, 5, 86) (dual of [(33, 5), 13, 87]-NRT-code)	[i]		OOA Folding