MinT - Information on Result #1647346

Information on Result #1647346

Linear OOA(3¹⁹⁰, 3066581, F₃, 5, 18) (dual of [(3066581, 5), 15332715, 19]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(3¹⁹⁰, 3066581, F₃, 2, 18) (dual of [(3066581, 2), 6132972, 19]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(3¹⁹⁰, 4194308, F₃, 2, 18) (dual of [(4194308, 2), 8388426, 19]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(3¹⁰, 7, F₃, 2, 9) (dual of [(7, 2), 4, 10]-NRT-code), using
    - extended algebraic-geometric NRT-code AG_e(2;F,4P) [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(3¹⁸⁰, 4194301, F₃, 2, 18) (dual of [(4194301, 2), 8388422, 19]-NRT-code), using
    - OOA 2-folding [i] based on linear OA(3¹⁸⁰, 8388602, F₃, 18) (dual of [8388602, 8388422, 19]-code), using
      - discarding factors / shortening the dual code based on linear OA(3¹⁸⁰, large, F₃, 18) (dual of [large, large−180, 19]-code), using
        the primitive narrow-sense BCH-code C(I) with length 14348906Â = 3¹⁵âˆ’1, defining interval IÂ =Â [1,18], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 19 [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(3¹⁹⁰, 1533290, F₃, 25, 18) (dual of [(1533290, 25), 38332060, 19]-NRT-code)	[i]		OOA Folding and Stacking with Additional Row