MinT - Information on Result #2781368

Information on Result #2781368

Linear OOA(2²¹³, 54, F₂, 4, 180) (dual of [(54, 4), 3, 181]-NRT-code), using 16 step truncation based on linear OOA(2²²⁹, 58, F₂, 4, 196) (dual of [(58, 4), 3, 197]-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(2²¹⁷, 55, F₂, 4, 186) (dual of [(55, 4), 3, 187]-NRT-code), using
  - repeating each code word 11 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(2²¹³, 27, F₂, 8, 180) (dual of [(27, 8), 3, 181]-NRT-code)	[i]		OOA Folding