MinT - Information on Result #1421759

Information on Result #1421759

Linear OOA(4¹⁰⁹, 189667, F₄, 2, 15) (dual of [(189667, 2), 379225, 16]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OA(4¹⁰⁹, 189667, F₄, 15) (dual of [189667, 189558, 16]-code), using

discarding factors / shortening the dual code based on linear OA(4¹⁰⁹, 262161, F₄, 15) (dual of [262161, 262052, 16]-code), using
- (u,Â u+v)-construction [i] based on
  1. 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]
  2. linear OA(4¹⁰⁰, 262144, F₄, 15) (dual of [262144, 262044, 16]-code), using
    - an extension C_e(14) of the primitive narrow-sense BCH-code C(I) with length 262143Â = 4⁹âˆ’1, defining interval IÂ =Â [1,14], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 15 [i]

Mode: 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(4¹⁰⁹, 94833, F₄, 3, 15) (dual of [(94833, 3), 284390, 16]-NRT-code)	[i]		OOA Folding