MinT - Information on Result #964478

Information on Result #964478

Linear OOA(4¹⁷³, 352, F₄, 3, 44) (dual of [(352, 3), 883, 45]-NRT-code), using OOA 3-folding based on linear OA(4¹⁷³, 1056, F₄, 44) (dual of [1056, 883, 45]-code), using

discarding factors / shortening the dual code based on linear OA(4¹⁷³, 1058, F₄, 44) (dual of [1058, 885, 45]-code), using
- constructionÂ XX applied to C₁Â =Â C([1019,36]), C₂Â =Â C([0,40]), C₃Â =Â C₁Â +Â C₂Â =Â C([0,36]), and C_âˆ©Â =Â C₁Â âˆ©Â C₂Â =Â C([1019,40]) [i] based on
  1. linear OA(4¹⁵¹, 1023, F₄, 41) (dual of [1023, 872, 42]-code), using the primitive BCH-code C(I) with length 1023Â = 4⁵âˆ’1, defining interval IÂ =Â {−4,−3,…,36}, and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 42 [i]
  2. linear OA(4¹⁵¹, 1023, F₄, 41) (dual of [1023, 872, 42]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 1023Â = 4⁵âˆ’1, defining interval IÂ =Â [0,40], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 42 [i]
  3. linear OA(4¹⁶⁶, 1023, F₄, 45) (dual of [1023, 857, 46]-code), using the primitive BCH-code C(I) with length 1023Â = 4⁵âˆ’1, defining interval IÂ =Â {−4,−3,…,40}, and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 46 [i]
  4. linear OA(4¹³⁶, 1023, F₄, 37) (dual of [1023, 887, 38]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 1023Â = 4⁵âˆ’1, defining interval IÂ =Â [0,36], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 38 [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, 18, F₄, 2) (dual of [18, 15, 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.