MinT - Information on Result #918159

Information on Result #918159

Linear OOA(4¹⁸⁴, 100, F₄, 2, 127) (dual of [(100, 2), 16, 128]-NRT-code), using concatenation of two NRT-codes based on

linear OOA(16³², 20, F₁₆, 2, 31) (dual of [(20, 2), 8, 32]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(16³², 24, F₁₆, 2, 31) (dual of [(24, 2), 16, 32]-NRT-code), using
  - extended algebraic-geometric NRT-code AG_e(2;F,16P) [i] based on function field F/F₁₆ with g(F) = 1 and N(F) ≥ 24, using
    - a function field by SÃ©mirat [i]
linear OA(4³, 5, F₄, 3) (dual of [5, 2, 4]-code or 5-arc in PG(2,4) or 5-cap in PG(2,4)), using
- extended Reedâ€“Solomon code RS_e(2,4) [i]
- Simplex code S(2,4) [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		This result only	Method
1	Linear OOA(4¹⁸⁴, 100, F₄, 2, 126) (dual of [(100, 2), 16, 127]-NRT-code)	[i]		Strength Reduction for OOAs
2	Linear OOA(4¹⁸⁴, 100, F₄, 2, 125) (dual of [(100, 2), 16, 126]-NRT-code)	[i]
3	Linear OOA(4¹⁸⁴, 100, F₄, 2, 124) (dual of [(100, 2), 16, 125]-NRT-code)	[i]
4	Linear OOA(4¹⁸³, 99, F₄, 2, 126) (dual of [(99, 2), 15, 127]-NRT-code)	[i]		Truncation for OOAs
5	Linear OOA(4¹⁸², 99, F₄, 2, 125) (dual of [(99, 2), 16, 126]-NRT-code)	[i]
6	Linear OOA(4¹⁸¹, 98, F₄, 2, 124) (dual of [(98, 2), 15, 125]-NRT-code)	[i]
7	Linear OOA(4¹⁸⁰, 98, F₄, 2, 123) (dual of [(98, 2), 16, 124]-NRT-code)	[i]
8	Linear OOA(4¹⁷⁹, 97, F₄, 2, 122) (dual of [(97, 2), 15, 123]-NRT-code)	[i]
9	Linear OOA(4¹⁷⁸, 97, F₄, 2, 121) (dual of [(97, 2), 16, 122]-NRT-code)	[i]
10	Linear OOA(4¹⁷⁷, 96, F₄, 2, 120) (dual of [(96, 2), 15, 121]-NRT-code)	[i]
11	Linear OOA(4¹⁷³, 94, F₄, 2, 116) (dual of [(94, 2), 15, 117]-NRT-code)	[i]