MinT - Information on Result #2428623

Information on Result #2428623

Linear OOA(2²⁴⁹, 126, F₂, 2, 173) (dual of [(126, 2), 3, 174]-NRT-code), using strength reduction based on linear OOA(2²⁴⁹, 126, F₂, 2, 175) (dual of [(126, 2), 3, 176]-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(2²⁴³, 123, F₂, 2, 171) (dual of [(123, 2), 3, 172]-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(2²³⁷, 120, F₂, 2, 167) (dual of [(120, 2), 3, 168]-NRT-code), using
      - repeating each code word 24 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(2²⁴⁹, 63, F₂, 4, 173) (dual of [(63, 4), 3, 174]-NRT-code)	[i]		OOA Folding