MinT - Information on Result #907990

Information on Result #907990

Linear OOA(4¹³⁹, 72, F₄, 2, 107) (dual of [(72, 2), 5, 108]-NRT-code), using repeating each code word 2 times based on linear OOA(4⁶⁷, 36, F₄, 2, 53) (dual of [(36, 2), 5, 54]-NRT-code), using

generalized (u,Â u+v)-construction [i] based on
1. linear OOA(4¹⁴, 9, F₄, 2, 13) (dual of [(9, 2), 4, 14]-NRT-code), using
  - extended algebraic-geometric NRT-code AG_e(2;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(4¹⁷, 9, F₄, 2, 17) (dual of [(9, 2), 1, 18]-NRT-code), using
  - dual of repetition NRT-code with length 9 [i]
3. linear OOA(4¹⁸, 9, F₄, 2, 18) (dual of [(9, 2), 0, 19]-NRT-code), using
  - complete OOA / dual of NRT-code with only one code word [i]
4. linear OOA(4¹⁸, 9, F₄, 2, 18) (dual of [(9, 2), 0, 19]-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		Method
1	Linear OOA(4¹³⁹, 72, F₄, 2, 106) (dual of [(72, 2), 5, 107]-NRT-code)	[i]	Strength Reduction for OOAs
2	Linear OOA(4¹³⁹, 72, F₄, 2, 105) (dual of [(72, 2), 5, 106]-NRT-code)	[i]	Strength Reduction for OOAs
3	Linear OOA(4¹⁵⁷, 81, F₄, 2, 120) (dual of [(81, 2), 5, 121]-NRT-code)	[i]	Juxtaposition for OOAs
4	Linear OOA(4¹⁶⁵, 85, F₄, 2, 126) (dual of [(85, 2), 5, 127]-NRT-code)	[i]
5	Linear OOA(4¹⁶⁷, 86, F₄, 2, 128) (dual of [(86, 2), 5, 129]-NRT-code)	[i]