MinT - Information on Result #1024654

Information on Result #1024654

Linear OOA(4²⁶⁰, 88, F₄, 3, 223) (dual of [(88, 3), 4, 224]-NRT-code), using repeating each code word 2 times based on linear OOA(4¹²⁸, 44, F₄, 3, 111) (dual of [(44, 3), 4, 112]-NRT-code), using

6 step truncation [i] based on linear OOA(4¹³⁴, 46, F₄, 3, 117) (dual of [(46, 3), 4, 118]-NRT-code), using
- juxtaposition [i] based on
  1. linear OOA(4²³, 9, F₄, 3, 22) (dual of [(9, 3), 4, 23]-NRT-code), using
    - extended algebraic-geometric NRT-code AG_e(3;F,4P) [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(4¹⁰⁷, 37, F₄, 3, 94) (dual of [(37, 3), 4, 95]-NRT-code), using
    - juxtaposition [i] based on
      1. linear OOA(4²³, 9, F₄, 3, 22) (dual of [(9, 3), 4, 23]-NRT-code) (see above)
      2. linear OOA(4⁸⁰, 28, F₄, 3, 71) (dual of [(28, 3), 4, 72]-NRT-code), using
        repeating each code word 2 times [i] based on linear OOA(4³⁸, 14, F₄, 3, 35) (dual of [(14, 3), 4, 36]-NRT-code), using
        extended algebraic-geometric NRT-code AG_e(3;F,6P) [i] based on function field F/F₄ with g(F) = 3 and N(F) ≥ 14, 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		Method
1	Linear OOA(4²⁶⁰, 88, F₄, 3, 222) (dual of [(88, 3), 4, 223]-NRT-code)	[i]	Strength Reduction for OOAs
2	Linear OOA(4²⁶⁰, 88, F₄, 3, 221) (dual of [(88, 3), 4, 222]-NRT-code)	[i]
3	Linear OOA(4²⁶⁰, 88, F₄, 3, 220) (dual of [(88, 3), 4, 221]-NRT-code)	[i]
4	Linear OOA(4²⁵⁶, 86, F₄, 3, 219) (dual of [(86, 3), 2, 220]-NRT-code)	[i]	Truncation for OOAs
5	Linear OOA(4²⁴⁷, 83, F₄, 3, 210) (dual of [(83, 3), 2, 211]-NRT-code)	[i]
6	Linear OOA(4²⁴⁵, 83, F₄, 3, 208) (dual of [(83, 3), 4, 209]-NRT-code)	[i]
7	Linear OOA(4²⁴⁴, 82, F₄, 3, 207) (dual of [(82, 3), 2, 208]-NRT-code)	[i]
8	Linear OOA(4²⁴², 82, F₄, 3, 205) (dual of [(82, 3), 4, 206]-NRT-code)	[i]