MinT - Information on Result #918048

Information on Result #918048

Linear OOA(4²⁴⁴, 144, F₄, 2, 143) (dual of [(144, 2), 44, 144]-NRT-code), using concatenation of two NRT-codes based on

linear OOA(16⁵⁰, 36, F₁₆, 2, 47) (dual of [(36, 2), 22, 48]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(16⁵⁰, 38, F₁₆, 2, 47) (dual of [(38, 2), 26, 48]-NRT-code), using
  - extended algebraic-geometric NRT-code AG_e(2;F,28P) [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(4²⁴⁴, 144, F₄, 2, 142) (dual of [(144, 2), 44, 143]-NRT-code)	[i]		Strength Reduction for OOAs
2	Linear OOA(4²⁴⁴, 144, F₄, 2, 141) (dual of [(144, 2), 44, 142]-NRT-code)	[i]		Strength Reduction for OOAs
3	Linear OOA(4²⁴⁵, 144, F₄, 2, 143) (dual of [(144, 2), 43, 144]-NRT-code)	[i]		OOA Duplication
4	Linear OOA(4²⁴³, 143, F₄, 2, 142) (dual of [(143, 2), 43, 143]-NRT-code)	[i]		Truncation for OOAs
5	Linear OOA(4²⁴², 143, F₄, 2, 141) (dual of [(143, 2), 44, 142]-NRT-code)	[i]
6	Linear OOA(4²⁴¹, 142, F₄, 2, 140) (dual of [(142, 2), 43, 141]-NRT-code)	[i]
7	Linear OOA(4²⁴⁰, 142, F₄, 2, 139) (dual of [(142, 2), 44, 140]-NRT-code)	[i]
8	Linear OOA(4²³⁹, 141, F₄, 2, 138) (dual of [(141, 2), 43, 139]-NRT-code)	[i]
9	Linear OOA(4²³⁸, 141, F₄, 2, 137) (dual of [(141, 2), 44, 138]-NRT-code)	[i]
10	Linear OOA(4²³⁷, 140, F₄, 2, 136) (dual of [(140, 2), 43, 137]-NRT-code)	[i]