MinT - Information on Result #1058559

Information on Result #1058559

Linear OOA(2¹⁴⁹, 38, F₂, 4, 105) (dual of [(38, 4), 3, 106]-NRT-code), using OOA 2-folding based on linear OOA(2¹⁴⁹, 76, F₂, 2, 105) (dual of [(76, 2), 3, 106]-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(2¹⁴³, 73, F₂, 2, 101) (dual of [(73, 2), 3, 102]-NRT-code), using
  - juxtaposition [i] based on
    1. linear OOA(2³, 3, F₂, 2, 3) (dual of [(3, 2), 3, 4]-NRT-code) (see above)
    2. linear OOA(2¹³⁷, 70, F₂, 2, 97) (dual of [(70, 2), 3, 98]-NRT-code), using
      - repeating each code word 14 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(2²⁴⁰, 71, F₂, 4, 105) (dual of [(71, 4), 44, 106]-NRT-code)	[i]		(u,Â u+v)-Construction for OOAs
2	Linear OOA(2²⁵⁵, 76, F₂, 4, 105) (dual of [(76, 4), 49, 106]-NRT-code)	[i]		(u,Â u+v)-Construction for OOAs