MinT - Information on Result #1605470

Information on Result #1605470

Linear OOA(3¹⁵⁶, 4194382, F₃, 4, 14) (dual of [(4194382, 4), 16777372, 15]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(3¹⁵⁶, 4194382, F₃, 2, 14) (dual of [(4194382, 2), 8388608, 15]-NRT-code), using

(u,Â u+v)-construction [i] based on
1. linear OOA(3²⁰, 81, F₃, 2, 7) (dual of [(81, 2), 142, 8]-NRT-code), using
  - embedding of OOA with Gilbertâ€“VarÅ¡amov bound [i] based on linear OA(3²⁰, 81, F₃, 7) (dual of [81, 61, 8]-code), using
    - discarding factors / shortening the dual code based on linear OA(3²⁰, 121, F₃, 7) (dual of [121, 101, 8]-code), using
      - the BCH-code C(I) with length 121Â | 3⁵âˆ’1, defining interval IÂ =Â {−3,−1,1,…,9}, and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 8 [i]
2. linear OOA(3¹³⁶, 4194301, F₃, 2, 14) (dual of [(4194301, 2), 8388466, 15]-NRT-code), using
  - OOA 2-folding [i] based on linear OA(3¹³⁶, 8388602, F₃, 14) (dual of [8388602, 8388466, 15]-code), using
    - discarding factors / shortening the dual code based on linear OA(3¹³⁶, large, F₃, 14) (dual of [large, large−136, 15]-code), using
      - the primitive expurgated narrow-sense BCH-code C(I) with length 14348906Â = 3¹⁵âˆ’1, defining interval IÂ =Â [0,13], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 15 [i]

Mode: Linear.

Optimality

Show details for fixed k and m, k and s, k and t, m and s, m 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(3¹⁵⁶, 2097190, F₃, 20, 14) (dual of [(2097190, 20), 41943644, 15]-NRT-code)	[i]		OOA Folding and Stacking with Additional Row