MinT - Information on Result #2766513

Information on Result #2766513

Linear OOA(2²³⁴, 60, F₂, 4, 177) (dual of [(60, 4), 6, 178]-NRT-code), using strength reduction based on linear OOA(2²³⁴, 60, F₂, 4, 178) (dual of [(60, 4), 6, 179]-NRT-code), using

juxtaposition [i] based on
1. linear OOA(2²⁶, 8, F₂, 4, 22) (dual of [(8, 4), 6, 23]-NRT-code), using
  - extended algebraic-geometric NRT-code AG_e(4;F,9P) [i] based on function field F/F₂ with g(F) = 4 and N(F) ≥ 8, using
    - an explicitly constructive algebraic function field [i]
2. linear OOA(2²⁰², 52, F₂, 4, 155) (dual of [(52, 4), 6, 156]-NRT-code), using
  - juxtaposition [i] based on
    1. linear OOA(2²², 7, F₂, 4, 19) (dual of [(7, 4), 6, 20]-NRT-code), using
      - extended algebraic-geometric NRT-code AG_e(4;F,8P) [i] based on function field F/F₂ with g(F) = 3 and N(F) ≥ 7, using
        an explicitly constructive algebraic function field [i]
    2. linear OOA(2¹⁷⁴, 45, F₂, 4, 135) (dual of [(45, 4), 6, 136]-NRT-code), using
      - concatenation of two NRT-codes [i] based on
        linear OA(8⁷, 9, F₈, 7) (dual of [9, 2, 8]-code or 9-arc in PG(6,8)), using
        extended Reedâ€“Solomon code RS_e(2,8) [i]
        Simplex code S(2,8) [i]
        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(2²³⁴, 30, F₂, 8, 177) (dual of [(30, 8), 6, 178]-NRT-code)	[i]		OOA Folding