MinT - Information on Result #1058609

Information on Result #1058609

Linear OOA(2¹⁵³, 39, F₂, 4, 107) (dual of [(39, 4), 3, 108]-NRT-code), using OOA 2-folding based on linear OOA(2¹⁵³, 78, F₂, 2, 107) (dual of [(78, 2), 3, 108]-NRT-code), using

strength reduction [i] based on linear OOA(2¹⁵³, 78, F₂, 2, 108) (dual of [(78, 2), 3, 109]-NRT-code), using
- juxtaposition [i] based on
  1. linear OOA(2³, 3, F₂, 2, 3) (dual of [(3, 2), 3, 4]-NRT-code), using
    - extended Reedâ€“Solomon NRT-code RS_e(2;3,2) [i]
  2. linear OOA(2¹⁴⁷, 75, F₂, 2, 104) (dual of [(75, 2), 3, 105]-NRT-code), using
    - repeating each code word 15 times [i] based on linear OOA(2⁷, 5, F₂, 2, 6) (dual of [(5, 2), 3, 7]-NRT-code), using
      - extended algebraic-geometric NRT-code AG_e(2;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(2²⁴⁵, 72, F₂, 4, 107) (dual of [(72, 4), 43, 108]-NRT-code)	[i]		(u,Â u+v)-Construction for OOAs
2	Linear OOA(2²⁶⁰, 78, F₂, 4, 107) (dual of [(78, 4), 52, 108]-NRT-code)	[i]		(u,Â u+v)-Construction for OOAs