MinT - Information on Result #706432

Information on Result #706432

Linear OA(4¹⁰⁸, 290, F₄, 34) (dual of [290, 182, 35]-code), using constructionÂ XX applied to C₁Â =Â C([69,101]), C₂Â =Â C([68,93]), C₃Â =Â C₁Â +Â C₂Â =Â C([69,93]), and C_âˆ©Â =Â C₁Â âˆ©Â C₂Â =Â C([68,101]) based on

linear OA(4⁹³, 255, F₄, 33) (dual of [255, 162, 34]-code), using the primitive BCH-code C(I) with length 255Â = 4⁴âˆ’1, defining interval IÂ =Â {69,70,…,101}, and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 34 [i]
linear OA(4⁷⁵, 255, F₄, 26) (dual of [255, 180, 27]-code), using the primitive BCH-code C(I) with length 255Â = 4⁴âˆ’1, defining interval IÂ =Â {68,69,…,93}, and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 27 [i]
linear OA(4⁹⁵, 255, F₄, 34) (dual of [255, 160, 35]-code), using the primitive BCH-code C(I) with length 255Â = 4⁴âˆ’1, defining interval IÂ =Â {68,69,…,101}, and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 35 [i]
linear OA(4⁷³, 255, F₄, 25) (dual of [255, 182, 26]-code), using the primitive BCH-code C(I) with length 255Â = 4⁴âˆ’1, defining interval IÂ =Â {69,70,…,93}, and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 26 [i]
linear OA(4¹³, 33, F₄, 7) (dual of [33, 20, 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]
linear OA(4⁰, 2, F₄, 0) (dual of [2, 2, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(4⁰, s, F₄, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
  - OA with only one run / dual of code without redundancy [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

The following results depend on this result:

	Result		This result only	Method
1	Linear OOA(4¹⁰⁸, 145, F₄, 2, 34) (dual of [(145, 2), 182, 35]-NRT-code)	[i]		OOA Folding