MinT - Information on Result #1602033

Information on Result #1602033

Linear OOA(3⁸¹, 4194309, F₃, 4, 8) (dual of [(4194309, 4), 16777155, 9]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(3⁸¹, 4194309, F₃, 2, 8) (dual of [(4194309, 2), 8388537, 9]-NRT-code), using

(u,Â u+v)-construction [i] based on
1. linear OOA(3⁵, 8, F₃, 2, 4) (dual of [(8, 2), 11, 5]-NRT-code), using
  - extracting embedded OOA [i] based on digital (1, 5, 8)-net over F₃, using
    - nets constructed from net-embeddable BCH codes [i]
2. linear OOA(3⁷⁶, 4194301, F₃, 2, 8) (dual of [(4194301, 2), 8388526, 9]-NRT-code), using
  - OOA 2-folding [i] based on linear OA(3⁷⁶, 8388602, F₃, 8) (dual of [8388602, 8388526, 9]-code), using
    - discarding factors / shortening the dual code based on linear OA(3⁷⁶, large, F₃, 8) (dual of [large, large−76, 9]-code), using
      - the primitive expurgated narrow-sense BCH-code C(I) with length 14348906Â = 3¹⁵âˆ’1, defining interval IÂ =Â [0,7], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 9 [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(3⁸¹, 4194308, F₃, 5, 8) (dual of [(4194308, 5), 20971459, 9]-NRT-code)	[i]		OOA Stacking with Additional Row
2	Linear OOA(3⁸¹, 4194308, F₃, 12, 8) (dual of [(4194308, 12), 50331615, 9]-NRT-code)	[i]		OOA Stacking with Additional Row