MinT - Information on Result #706502

Information on Result #706502

Linear OA(4¹¹⁴, 290, F₄, 36) (dual of [290, 176, 37]-code), using constructionÂ XX applied to C₁Â =Â C([51,85]), C₂Â =Â C([59,86]), C₃Â =Â C₁Â +Â C₂Â =Â C([59,85]), and C_âˆ©Â =Â C₁Â âˆ©Â C₂Â =Â C([51,86]) based on

linear OA(4⁹⁷, 255, F₄, 35) (dual of [255, 158, 36]-code), using the primitive BCH-code C(I) with length 255Â = 4⁴âˆ’1, defining interval IÂ =Â {51,52,…,85}, and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 36 [i]
linear OA(4⁸³, 255, F₄, 28) (dual of [255, 172, 29]-code), using the primitive BCH-code C(I) with length 255Â = 4⁴âˆ’1, defining interval IÂ =Â {59,60,…,86}, and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 29 [i]
linear OA(4¹⁰¹, 255, F₄, 36) (dual of [255, 154, 37]-code), using the primitive BCH-code C(I) with length 255Â = 4⁴âˆ’1, defining interval IÂ =Â {51,52,…,86}, and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 37 [i]
linear OA(4⁷⁹, 255, F₄, 27) (dual of [255, 176, 28]-code), using the primitive BCH-code C(I) with length 255Â = 4⁴âˆ’1, defining interval IÂ =Â {59,60,…,85}, and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 28 [i]
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]
linear OA(4⁰, 4, F₄, 0) (dual of [4, 4, 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(4¹¹⁴, 145, F₄, 2, 36) (dual of [(145, 2), 176, 37]-NRT-code)	[i]		OOA Folding