MinT - Information on Result #706454

Information on Result #706454

Linear OA(4¹¹³, 294, F₄, 35) (dual of [294, 181, 36]-code), using constructionÂ XX applied to C₁Â =Â C([52,84]), C₂Â =Â C([60,86]), C₃Â =Â C₁Â +Â C₂Â =Â C([60,84]), and C_âˆ©Â =Â C₁Â âˆ©Â C₂Â =Â C([52,86]) based on

linear OA(4⁹⁴, 255, F₄, 33) (dual of [255, 161, 34]-code), using the primitive BCH-code C(I) with length 255Â = 4⁴âˆ’1, defining interval IÂ =Â {52,53,…,84}, and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 34 [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 {60,61,…,86}, and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 28 [i]
linear OA(4⁹⁹, 255, F₄, 35) (dual of [255, 156, 36]-code), using the primitive BCH-code C(I) with length 255Â = 4⁴âˆ’1, defining interval IÂ =Â {52,53,…,86}, and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 36 [i]
linear OA(4⁷⁴, 255, F₄, 25) (dual of [255, 181, 26]-code), using the primitive BCH-code C(I) with length 255Â = 4⁴âˆ’1, defining interval IÂ =Â {60,61,…,84}, 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(4¹, 6, F₄, 1) (dual of [6, 5, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(4¹, s, F₄, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
  - parity-check code [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(4¹¹³, 147, F₄, 2, 35) (dual of [(147, 2), 181, 36]-NRT-code)	[i]		OOA Folding