MinT - Information on Result #2439509

Information on Result #2439509

Linear OOA(4¹⁰⁵, 56, F₄, 2, 78) (dual of [(56, 2), 7, 79]-NRT-code), using strength reduction based on linear OOA(4¹⁰⁵, 56, F₄, 2, 79) (dual of [(56, 2), 7, 80]-NRT-code), using

generalized (u,Â u+v)-construction [i] based on
1. 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, using
    - an explicitly constructive algebraic function field [i]
2. linear OOA(4²⁷, 14, F₄, 2, 26) (dual of [(14, 2), 1, 27]-NRT-code), using
  - strength reduction [i] based on linear OOA(4²⁷, 14, F₄, 2, 27) (dual of [(14, 2), 1, 28]-NRT-code), using
    - dual of repetition NRT-code with length 14 [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(4¹⁰³, 55, F₄, 2, 76) (dual of [(55, 2), 7, 77]-NRT-code)	[i]		Truncation for OOAs