MinT - Information on Result #2425567

Information on Result #2425567

Linear OOA(2²¹⁶, 110, F₂, 2, 144) (dual of [(110, 2), 4, 145]-NRT-code), using strength reduction based on linear OOA(2²¹⁶, 110, F₂, 2, 145) (dual of [(110, 2), 4, 146]-NRT-code), using

juxtaposition [i] based on
1. linear OOA(2⁶, 5, F₂, 2, 5) (dual of [(5, 2), 4, 6]-NRT-code), using
  - extended algebraic-geometric NRT-code AG_e(2;F,4P) [i] based on function field F/F₂ with g(F) = 1 and N(F) ≥ 5, using
    - an explicitly constructive algebraic function field [i]
2. linear OOA(2²⁰⁶, 105, F₂, 2, 139) (dual of [(105, 2), 4, 140]-NRT-code), using
  - concatenation of two NRT-codes [i] based on
    1. linear OA(4³³, 35, F₄, 27) (dual of [35, 2, 28]-code), using
      - repeating each code word 7 times [i] based on linear OA(4³, 5, F₄, 3) (dual of [5, 2, 4]-code or 5-arc in PG(2,4) or 5-cap in PG(2,4)), using
        extended Reedâ€“Solomon code RS_e(2,4) [i]
        Simplex code S(2,4) [i]
    2. linear OOA(2⁴, 3, F₂, 2, 4) (dual of [(3, 2), 2, 5]-NRT-code), using
      - extended Reedâ€“Solomon NRT-code RS_e(2;2,2) [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(2²¹⁶, 55, F₂, 4, 144) (dual of [(55, 4), 4, 145]-NRT-code)	[i]		OOA Folding