| Summary: | Let <i>p</i> be an odd prime, where <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>ϑ</mi></semantics></math></inline-formula> and <i>m</i> are positive integers. Let <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>ψ</mi></semantics></math></inline-formula> be a nonzero element of the finite field <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi mathvariant="double-struck">F</mi><mi>q</mi></msub></semantics></math></inline-formula>, where <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>q</mi><mo>=</mo><msup><mi>p</mi><mi>m</mi></msup></mrow></semantics></math></inline-formula>, and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi mathvariant="fraktur">R</mi><mo>=</mo><msub><mi mathvariant="double-struck">F</mi><mi>q</mi></msub><mo>+</mo><mi>u</mi><msub><mi mathvariant="double-struck">F</mi><mi>q</mi></msub><mo>+</mo><msup><mi>u</mi><mn>2</mn></msup><msub><mi mathvariant="double-struck">F</mi><mi>q</mi></msub><mspace width="0.166667em"></mspace><mspace width="0.166667em"></mspace><mrow><mo stretchy="false">(</mo><msup><mi>u</mi><mn>3</mn></msup><mo>=</mo><mn>0</mn><mo stretchy="false">)</mo></mrow></mrow></semantics></math></inline-formula>. In this paper, we determine completely the symbol-triple distances of all <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>ψ</mi></semantics></math></inline-formula>-constacyclic codes of length <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mi>p</mi><mi>ϑ</mi></msup></semantics></math></inline-formula> over <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="fraktur">R</mi></semantics></math></inline-formula>.
|
|---|