MinT - Information on Result #1647423

Information on Result #1647423

Linear OOA(3¹⁹¹, 3299610, F₃, 5, 18) (dual of [(3299610, 5), 16497859, 19]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(3¹⁹¹, 3299610, F₃, 2, 18) (dual of [(3299610, 2), 6599029, 19]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(3¹⁹¹, 4194309, F₃, 2, 18) (dual of [(4194309, 2), 8388427, 19]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(3¹¹, 8, F₃, 2, 9) (dual of [(8, 2), 5, 10]-NRT-code), using
    - extended algebraic-geometric NRT-code AG_e(2;F,6P) [i] based on function field F/F₃ with g(F) = 2 and N(F) ≥ 8, 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(3¹⁹¹, 1649804, F₃, 25, 18) (dual of [(1649804, 25), 41244909, 19]-NRT-code)	[i]		OOA Folding and Stacking with Additional Row