MinT - Information on Result #1062685

Information on Result #1062685

Linear OOA(3¹⁶¹, 189, F₃, 4, 40) (dual of [(189, 4), 595, 41]-NRT-code), using OOA 4-folding based on linear OA(3¹⁶¹, 756, F₃, 40) (dual of [756, 595, 41]-code), using

discarding factors / shortening the dual code based on linear OA(3¹⁶¹, 757, F₃, 40) (dual of [757, 596, 41]-code), using
- constructionÂ XX applied to C₁Â =Â C([725,33]), C₂Â =Â C([0,36]), C₃Â =Â C₁Â +Â C₂Â =Â C([0,33]), and C_âˆ©Â =Â C₁Â âˆ©Â C₂Â =Â C([725,36]) [i] based on
  1. linear OA(3¹⁴², 728, F₃, 37) (dual of [728, 586, 38]-code), using the primitive BCH-code C(I) with length 728Â = 3⁶âˆ’1, defining interval IÂ =Â {−3,−2,…,33}, and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 38 [i]
  2. linear OA(3¹⁴², 728, F₃, 37) (dual of [728, 586, 38]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 728Â = 3⁶âˆ’1, defining interval IÂ =Â [0,36], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 38 [i]
  3. linear OA(3¹⁵⁴, 728, F₃, 40) (dual of [728, 574, 41]-code), using the primitive BCH-code C(I) with length 728Â = 3⁶âˆ’1, defining interval IÂ =Â {−3,−2,…,36}, and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 41 [i]
  4. linear OA(3¹³⁰, 728, F₃, 34) (dual of [728, 598, 35]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 728Â = 3⁶âˆ’1, defining interval IÂ =Â [0,33], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 35 [i]
  5. linear OA(3³, 13, F₃, 2) (dual of [13, 10, 3]-code), using
    - Hamming code H(3,3) [i]
  6. linear OA(3⁴, 16, F₃, 2) (dual of [16, 12, 3]-code), using
    - discarding factors / shortening the dual code based on linear OA(3⁴, 40, F₃, 2) (dual of [40, 36, 3]-code), using
      - Hamming code H(4,3) [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

None.