MinT - Information on Result #2764655

Information on Result #2764655

Linear OOA(2²⁰⁵, 52, F₂, 4, 172) (dual of [(52, 4), 3, 173]-NRT-code), using strength reduction based on linear OOA(2²⁰⁵, 52, F₂, 4, 175) (dual of [(52, 4), 3, 176]-NRT-code), using

juxtaposition [i] based on
1. linear OOA(2⁹, 3, F₂, 4, 9) (dual of [(3, 4), 3, 10]-NRT-code), using
  - extended Reedâ€“Solomon NRT-code RS_e(4;3,2) [i]
2. linear OOA(2¹⁹³, 49, F₂, 4, 165) (dual of [(49, 4), 3, 166]-NRT-code), using
  - 4 step truncation [i] based on linear OOA(2¹⁹⁷, 50, F₂, 4, 169) (dual of [(50, 4), 3, 170]-NRT-code), using
    - repeating each code word 10 times [i] based on linear OOA(2¹⁷, 5, F₂, 4, 16) (dual of [(5, 4), 3, 17]-NRT-code), using
      - extended algebraic-geometric NRT-code AG_e(4;F,3P) [i] based on function field F/F₂ with g(F) = 1 and N(F) ≥ 5, using
        an explicitly constructive algebraic function field [i]

Mode: Constructive and linear.

Optimality

Show details for fixed k and m, n and k, k and s, k and t, n and m, m and s, m and t, n and s, n 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(2²⁰⁵, 26, F₂, 8, 172) (dual of [(26, 8), 3, 173]-NRT-code)	[i]		OOA Folding