MinT - Information on Result #828182

Information on Result #828182

Linear OOA(4²⁰⁸, 526, F₄, 2, 54) (dual of [(526, 2), 844, 55]-NRT-code), using OOA 2-folding based on linear OA(4²⁰⁸, 1052, F₄, 54) (dual of [1052, 844, 55]-code), using

discarding factors / shortening the dual code based on linear OA(4²⁰⁸, 1053, F₄, 54) (dual of [1053, 845, 55]-code), using
- constructionÂ XX applied to C₁Â =Â C([1019,46]), C₂Â =Â C([0,49]), C₃Â =Â C₁Â +Â C₂Â =Â C([0,46]), and C_âˆ©Â =Â C₁Â âˆ©Â C₂Â =Â C([1019,49]) [i] based on
  1. linear OA(4¹⁹¹, 1023, F₄, 51) (dual of [1023, 832, 52]-code), using the primitive BCH-code C(I) with length 1023Â = 4⁵âˆ’1, defining interval IÂ =Â {−4,−3,…,46}, and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 52 [i]
  2. linear OA(4¹⁸⁶, 1023, F₄, 50) (dual of [1023, 837, 51]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 1023Â = 4⁵âˆ’1, defining interval IÂ =Â [0,49], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 51 [i]
  3. linear OA(4²⁰¹, 1023, F₄, 54) (dual of [1023, 822, 55]-code), using the primitive BCH-code C(I) with length 1023Â = 4⁵âˆ’1, defining interval IÂ =Â {−4,−3,…,49}, and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 55 [i]
  4. linear OA(4¹⁷⁶, 1023, F₄, 47) (dual of [1023, 847, 48]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 1023Â = 4⁵âˆ’1, defining interval IÂ =Â [0,46], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 48 [i]
  5. 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]
  6. linear OA(4³, 13, F₄, 2) (dual of [13, 10, 3]-code), using
    - discarding factors / shortening the dual code based on linear OA(4³, 21, F₄, 2) (dual of [21, 18, 3]-code), using
      - Hamming code H(3,4) [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.