MinT - Information on Result #909766

Information on Result #909766

Linear OOA(4¹⁶⁹, 87, F₄, 2, 129) (dual of [(87, 2), 5, 130]-NRT-code), using juxtaposition based on

linear OOA(4²³, 14, F₄, 2, 20) (dual of [(14, 2), 5, 21]-NRT-code), using
- extended algebraic-geometric NRT-code AG_e(2;F,7P) [i] based on function field F/F₄ with g(F) = 3 and N(F) ≥ 14, using
  - an explicitly constructive algebraic function field [i]
linear OOA(4¹⁴¹, 73, F₄, 2, 108) (dual of [(73, 2), 5, 109]-NRT-code), using
- juxtaposition [i] based on
  1. linear OOA(4¹³, 9, F₄, 2, 12) (dual of [(9, 2), 5, 13]-NRT-code), using
    - extended algebraic-geometric NRT-code AG_e(2;F,5P) [i] based on function field F/F₄ with g(F) = 1 and N(F) ≥ 9, using
      - the Hermitian function field over F₄ [i]
  2. linear OOA(4¹²³, 64, F₄, 2, 95) (dual of [(64, 2), 5, 96]-NRT-code), using
    - generalized (u,Â u+v)-construction [i] based on
      1. linear OOA(4²⁸, 16, F₄, 2, 23) (dual of [(16, 2), 4, 24]-NRT-code), using
        discarding factors / shortening the dual code based on linear OOA(4²⁸, 17, F₄, 2, 23) (dual of [(17, 2), 6, 24]-NRT-code), using
        extended algebraic-geometric NRT-code AG_e(2;F,10P) [i] based on function field F/F₄ with g(F) = 5 and N(F) ≥ 17, using
        an explicitly constructive algebraic function field [i]
      2. linear OOA(4³¹, 16, F₄, 2, 31) (dual of [(16, 2), 1, 32]-NRT-code), using
        dual of repetition NRT-code with length 16 [i]
      3. linear OOA(4³², 16, F₄, 2, 32) (dual of [(16, 2), 0, 33]-NRT-code), using
        complete OOA / dual of NRT-code with only one code word [i]
      4. linear OOA(4³², 16, F₄, 2, 32) (dual of [(16, 2), 0, 33]-NRT-code) (see above)

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(4¹⁹⁷, 101, F₄, 2, 150) (dual of [(101, 2), 5, 151]-NRT-code)	[i]		Juxtaposition for OOAs