MinT - Information on Result #2273423

Information on Result #2273423

Linear OA(4¹³¹, 303, F₄, 41) (dual of [303, 172, 42]-code), using 1 times code embedding in larger space based on linear OA(4¹³⁰, 302, F₄, 41) (dual of [302, 172, 42]-code), using

constructionÂ XX applied to C₁Â =Â C([49,85]), C₂Â =Â C([57,89]), C₃Â =Â C₁Â +Â C₂Â =Â C([57,85]), and C_âˆ©Â =Â C₁Â âˆ©Â C₂Â =Â C([49,89]) [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(4⁹⁵, 255, F₄, 33) (dual of [255, 160, 34]-code), using the primitive BCH-code C(I) with length 255Â = 4⁴âˆ’1, defining interval IÂ =Â {57,58,…,89}, and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 34 [i]
3. linear OA(4¹¹³, 255, F₄, 41) (dual of [255, 142, 42]-code), using the primitive BCH-code C(I) with length 255Â = 4⁴âˆ’1, defining interval IÂ =Â {49,50,…,89}, and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 42 [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(4⁴, 16, F₄, 3) (dual of [16, 12, 4]-code or 16-cap in PG(3,4)), using
  - discarding factors / shortening the dual code based on linear OA(4⁴, 17, F₄, 3) (dual of [17, 13, 4]-code or 17-cap in PG(3,4)) (see above)

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.