MinT - Information on Result #909760

Information on Result #909760

Linear OOA(4¹⁴⁵, 75, F₄, 2, 111) (dual of [(75, 2), 5, 112]-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(4¹¹⁷, 61, F₄, 2, 90) (dual of [(61, 2), 5, 91]-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(4⁹⁹, 52, F₄, 2, 77) (dual of [(52, 2), 5, 78]-NRT-code), using
    - generalized (u,Â u+v)-construction [i] based on
      1. linear OOA(4²², 13, F₄, 2, 19) (dual of [(13, 2), 4, 20]-NRT-code), using
        discarding factors / shortening the dual code based on linear OOA(4²², 14, F₄, 2, 19) (dual of [(14, 2), 6, 20]-NRT-code), using
        extended algebraic-geometric NRT-code AG_e(2;F,8P) [i] based on function field F/F₄ with g(F) = 3 and N(F) ≥ 14 (see above)
      2. linear OOA(4²⁵, 13, F₄, 2, 25) (dual of [(13, 2), 1, 26]-NRT-code), using
        dual of repetition NRT-code with length 13 [i]
      3. linear OOA(4²⁶, 13, F₄, 2, 26) (dual of [(13, 2), 0, 27]-NRT-code), using
        complete OOA / dual of NRT-code with only one code word [i]
      4. linear OOA(4²⁶, 13, F₄, 2, 26) (dual of [(13, 2), 0, 27]-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(4¹⁴⁵, 75, F₄, 2, 110) (dual of [(75, 2), 5, 111]-NRT-code)	[i]		Strength Reduction for OOAs