MinT - Information on Result #1610608

Information on Result #1610608

Linear OOA(3²²³, 2562000, F₃, 4, 22) (dual of [(2562000, 4), 10247777, 23]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(3²²³, 2562000, F₃, 3, 22) (dual of [(2562000, 3), 7685777, 23]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(3²²³, 2796208, F₃, 3, 22) (dual of [(2796208, 3), 8388401, 23]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(3¹², 7, F₃, 3, 11) (dual of [(7, 3), 9, 12]-NRT-code), using
    - extended algebraic-geometric NRT-code AG_e(3;F,9P) [i] based on function field F/F₃ with g(F) = 1 and N(F) ≥ 7, using
      - an explicitly constructive algebraic function field [i]
  2. linear OOA(3²¹¹, 2796201, F₃, 3, 22) (dual of [(2796201, 3), 8388392, 23]-NRT-code), using
    - OOA 3-folding [i] based on linear OA(3²¹¹, large, F₃, 22) (dual of [large, large−211, 23]-code), using
      - the primitive expurgated narrow-sense BCH-code C(I) with length 14348906Â = 3¹⁵âˆ’1, defining interval IÂ =Â [0,21], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 23 [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(3²²³, 853999, F₃, 28, 22) (dual of [(853999, 28), 23911749, 23]-NRT-code)	[i]		OOA Folding and Stacking with Additional Row