MinT - Information on Result #1522360

Information on Result #1522360

Linear OOA(3¹¹², 4194308, F₃, 3, 11) (dual of [(4194308, 3), 12582812, 12]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(3¹¹², 4194308, F₃, 2, 11) (dual of [(4194308, 2), 8388504, 12]-NRT-code), using

(u,Â u+v)-construction [i] based on
1. linear OOA(3⁶, 7, F₃, 2, 5) (dual of [(7, 2), 8, 6]-NRT-code), using
  - extended algebraic-geometric NRT-code AG_e(2;F,8P) [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(3¹⁰⁶, 4194301, F₃, 2, 11) (dual of [(4194301, 2), 8388496, 12]-NRT-code), using
  - OOA 2-folding [i] based on linear OA(3¹⁰⁶, 8388602, F₃, 11) (dual of [8388602, 8388496, 12]-code), using
    - discarding factors / shortening the dual code based on linear OA(3¹⁰⁶, large, F₃, 11) (dual of [large, large−106, 12]-code), using
      - the primitive expurgated narrow-sense BCH-code C(I) with length 14348906Â = 3¹⁵âˆ’1, defining interval IÂ =Â [0,10], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 12 [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(3¹¹², 2097154, F₃, 5, 11) (dual of [(2097154, 5), 10485658, 12]-NRT-code)	[i]		OOA Folding