MinT - Information on Result #2780107

Information on Result #2780107

Linear OOA(2⁵³, 14, F₂, 4, 45) (dual of [(14, 4), 3, 46]-NRT-code), using 8 step truncation based on linear OOA(2⁶¹, 16, F₂, 4, 53) (dual of [(16, 4), 3, 54]-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(2⁴⁹, 13, F₂, 4, 43) (dual of [(13, 4), 3, 44]-NRT-code), using
  - juxtaposition [i] based on
    1. linear OOA(2⁹, 3, F₂, 4, 9) (dual of [(3, 4), 3, 10]-NRT-code) (see above)
    2. linear OOA(2³⁷, 10, F₂, 4, 33) (dual of [(10, 4), 3, 34]-NRT-code), using
      - repeating each code word 2 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(2⁵³, 7, F₂, 8, 45) (dual of [(7, 8), 3, 46]-NRT-code)	[i]		OOA Folding