MinT - Information on Result #825966

Information on Result #825966

Linear OOA(4¹¹⁹, 146, F₄, 2, 38) (dual of [(146, 2), 173, 39]-NRT-code), using OOA 2-folding based on linear OA(4¹¹⁹, 292, F₄, 38) (dual of [292, 173, 39]-code), using

constructionÂ XX applied to C₁Â =Â C([49,84]), C₂Â =Â C([57,86]), C₃Â =Â C₁Â +Â C₂Â =Â C([57,84]), and C_âˆ©Â =Â C₁Â âˆ©Â C₂Â =Â C([49,86]) [i] based on
1. linear OA(4¹⁰⁰, 255, F₄, 36) (dual of [255, 155, 37]-code), using the primitive BCH-code C(I) with length 255Â = 4⁴âˆ’1, defining interval IÂ =Â {49,50,…,84}, and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 37 [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(4⁸², 255, F₄, 28) (dual of [255, 173, 29]-code), using the primitive BCH-code C(I) with length 255Â = 4⁴âˆ’1, defining interval IÂ =Â {57,58,…,84}, and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 29 [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(4¹, 6, F₄, 1) (dual of [6, 5, 2]-code), using
  - discarding factors / shortening the dual code based on linear OA(4¹, s, F₄, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
    - parity-check code [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.