MinT - Information on Result #822571

Information on Result #822571

Linear OOA(4¹³, 17, F₄, 2, 7) (dual of [(17, 2), 21, 8]-NRT-code), using OOA 2-folding 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
    1. 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]
    2. 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]

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.