MinT - Information on Result #825965

Information on Result #825965

Linear OOA(4¹¹⁸, 145, F₄, 2, 38) (dual of [(145, 2), 172, 39]-NRT-code), using OOA 2-folding based on linear OA(4¹¹⁸, 290, F₄, 38) (dual of [290, 172, 39]-code), using

constructionÂ XX applied to C₁Â =Â C([49,85]), C₂Â =Â C([57,86]), C₃Â =Â C₁Â +Â C₂Â =Â C([57,85]), and C_âˆ©Â =Â C₁Â âˆ©Â C₂Â =Â C([49,86]) [i] based on
1. linear OA(4¹⁰¹, 255, F₄, 37) (dual of [255, 154, 38]-code), using the primitive BCH-code C(I) with length 255Â = 4⁴âˆ’1, defining interval IÂ =Â {49,50,…,85}, and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 38 [i]
2. linear OA(4⁸⁷, 255, F₄, 30) (dual of [255, 168, 31]-code), using the primitive BCH-code C(I) with length 255Â = 4⁴âˆ’1, defining interval IÂ =Â {57,58,…,86}, and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 31 [i]
3. linear OA(4¹⁰⁵, 255, F₄, 38) (dual of [255, 150, 39]-code), using the primitive BCH-code C(I) with length 255Â = 4⁴âˆ’1, defining interval IÂ =Â {49,50,…,86}, and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 39 [i]
4. linear OA(4⁸³, 255, F₄, 29) (dual of [255, 172, 30]-code), using the primitive BCH-code C(I) with length 255Â = 4⁴âˆ’1, defining interval IÂ =Â {57,58,…,85}, and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 30 [i]
5. linear OA(4¹³, 31, F₄, 7) (dual of [31, 18, 8]-code), using
  - discarding factors / shortening the dual code based on linear OA(4¹³, 34, F₄, 7) (dual of [34, 21, 8]-code), using
    - (u,Â u+v)-construction [i] based on
      1. linear OA(4⁴, 17, F₄, 3) (dual of [17, 13, 4]-code or 17-cap in PG(3,4)), using
        ovoid in PG(3,Â 4) [i]
      2. linear OA(4⁹, 17, F₄, 7) (dual of [17, 8, 8]-code), using
        dual code (with bound on d by constructionÂ Y1) [i] based on
        linear OA(4⁸, 17, F₄, 6) (dual of [17, 9, 7]-code), using
        the BCH-code C(I) with length 17Â | 4⁴âˆ’1, defining interval IÂ =Â {1,4,7,…,16}, and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 7 [i]
        nonexistence of linear OA(4⁷, 10, F₄, 6) (dual of [10, 3, 7]-code), because
        bound for almost-MDS-codes with dimension nÂ =Â 3 [i]
6. linear OA(4⁰, 4, F₄, 0) (dual of [4, 4, 1]-code), using
  - discarding factors / shortening the dual code based on linear OA(4⁰, s, F₄, 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

None.