MinT - Information on Result #918194

Information on Result #918194

Linear OOA(4²²⁰, 115, F₄, 2, 163) (dual of [(115, 2), 10, 164]-NRT-code), using concatenation of two NRT-codes based on

linear OOA(16⁴¹, 23, F₁₆, 2, 40) (dual of [(23, 2), 5, 41]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(16⁴¹, 24, F₁₆, 2, 40) (dual of [(24, 2), 7, 41]-NRT-code), using
  - extended algebraic-geometric NRT-code AG_e(2;F,7P) [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(4²²⁰, 115, F₄, 2, 162) (dual of [(115, 2), 10, 163]-NRT-code)	[i]		Strength Reduction for OOAs
2	Linear OOA(4²¹⁹, 114, F₄, 2, 162) (dual of [(114, 2), 9, 163]-NRT-code)	[i]		Truncation for OOAs
3	Linear OOA(4²¹⁸, 114, F₄, 2, 161) (dual of [(114, 2), 10, 162]-NRT-code)	[i]
4	Linear OOA(4²¹⁷, 113, F₄, 2, 160) (dual of [(113, 2), 9, 161]-NRT-code)	[i]
5	Linear OOA(4²¹⁶, 113, F₄, 2, 159) (dual of [(113, 2), 10, 160]-NRT-code)	[i]
6	Linear OOA(4²¹⁵, 112, F₄, 2, 158) (dual of [(112, 2), 9, 159]-NRT-code)	[i]
7	Linear OOA(4²¹⁴, 112, F₄, 2, 157) (dual of [(112, 2), 10, 158]-NRT-code)	[i]
8	Linear OOA(4²¹³, 111, F₄, 2, 156) (dual of [(111, 2), 9, 157]-NRT-code)	[i]
9	Linear OOA(4²¹², 111, F₄, 2, 155) (dual of [(111, 2), 10, 156]-NRT-code)	[i]
10	Linear OOA(4²⁰⁹, 109, F₄, 2, 152) (dual of [(109, 2), 9, 153]-NRT-code)	[i]