MinT - Information on Result #918084

Information on Result #918084

Linear OOA(4²⁵⁴, 144, F₄, 2, 158) (dual of [(144, 2), 34, 159]-NRT-code), using concatenation of two NRT-codes based on

linear OOA(16⁵⁵, 36, F₁₆, 2, 52) (dual of [(36, 2), 17, 53]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(16⁵⁵, 38, F₁₆, 2, 52) (dual of [(38, 2), 21, 53]-NRT-code), using
  - extended algebraic-geometric NRT-code AG_e(2;F,23P) [i] based on function field F/F₁₆ with g(F) = 3 and N(F) ≥ 38, using
    - a function field by SÃ©mirat [i]
linear OA(4², 4, F₄, 2) (dual of [4, 2, 3]-code or 4-arc in PG(1,4)), using
- Reedâ€“Solomon code RS(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(4²⁵⁴, 144, F₄, 2, 157) (dual of [(144, 2), 34, 158]-NRT-code)	[i]		Strength Reduction for OOAs
2	Linear OOA(4²⁵⁴, 144, F₄, 2, 156) (dual of [(144, 2), 34, 157]-NRT-code)	[i]		Strength Reduction for OOAs
3	Linear OOA(4²⁵³, 143, F₄, 2, 157) (dual of [(143, 2), 33, 158]-NRT-code)	[i]		Truncation for OOAs
4	Linear OOA(4²⁵², 143, F₄, 2, 156) (dual of [(143, 2), 34, 157]-NRT-code)	[i]
5	Linear OOA(4²⁵¹, 142, F₄, 2, 155) (dual of [(142, 2), 33, 156]-NRT-code)	[i]
6	Linear OOA(4²⁵⁰, 142, F₄, 2, 154) (dual of [(142, 2), 34, 155]-NRT-code)	[i]
7	Linear OOA(4²⁴⁹, 141, F₄, 2, 153) (dual of [(141, 2), 33, 154]-NRT-code)	[i]
8	Linear OOA(4²⁴⁸, 141, F₄, 2, 152) (dual of [(141, 2), 34, 153]-NRT-code)	[i]
9	Linear OOA(4²⁴⁷, 140, F₄, 2, 151) (dual of [(140, 2), 33, 152]-NRT-code)	[i]