MinT - Information on Result #2439466

Information on Result #2439466

Linear OOA(4¹⁰³, 56, F₄, 2, 73) (dual of [(56, 2), 9, 74]-NRT-code), using strength reduction based on linear OOA(4¹⁰³, 56, F₄, 2, 74) (dual of [(56, 2), 9, 75]-NRT-code), using

generalized (u,Â u+v)-construction [i] based on
1. linear OOA(4²¹, 14, F₄, 2, 18) (dual of [(14, 2), 7, 19]-NRT-code), using
  - extended algebraic-geometric NRT-code AG_e(2;F,9P) [i] based on function field F/F₄ with g(F) = 3 and N(F) ≥ 14, using
    - an explicitly constructive algebraic function field [i]
2. linear OOA(4²⁶, 14, F₄, 2, 24) (dual of [(14, 2), 2, 25]-NRT-code), using
  - 2 step truncation [i] based on linear OOA(4²⁸, 15, F₄, 2, 26) (dual of [(15, 2), 2, 27]-NRT-code), using
    - repeating each code word 3 times [i] based on linear OOA(4⁸, 5, F₄, 2, 8) (dual of [(5, 2), 2, 9]-NRT-code), using
      - extended Reedâ€“Solomon NRT-code RS_e(2;2,4) [i]
3. linear OOA(4²⁸, 14, F₄, 2, 28) (dual of [(14, 2), 0, 29]-NRT-code), using
  - complete OOA / dual of NRT-code with only one code word [i]
4. linear OOA(4²⁸, 14, F₄, 2, 28) (dual of [(14, 2), 0, 29]-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(4¹⁰¹, 55, F₄, 2, 71) (dual of [(55, 2), 9, 72]-NRT-code)	[i]		Truncation for OOAs