MinT - Information on Result #629261

Information on Result #629261

Linear OA(2³³, 45, F₂, 15) (dual of [45, 12, 16]-code), using concatenation of two codes based on

linear OA(4⁹, 15, F₄, 7) (dual of [15, 6, 8]-code), using
- discarding factors / shortening the dual code based on 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
    1. 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]
    2. 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(2¹, 3, F₂, 1) (dual of [3, 2, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(2¹, s, F₂, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
  - parity-check code [i]

Mode: Constructive and linear.

None.

The following results depend on this result:

	Result		This result only	Method
1	Linear OA(2³², 44, F₂, 14) (dual of [44, 12, 15]-code)	[i]		Truncation
2	Linear OOA(2³³, 15, F₂, 3, 15) (dual of [(15, 3), 12, 16]-NRT-code)	[i]		OOA Folding