| Summary: | Let <i>p</i> be a prime, <i>s</i>, <i>m</i> be positive integers, <inline-formula><math display="inline"><semantics><mi>γ</mi></semantics></math></inline-formula> be a nonzero element of the finite field <inline-formula><math display="inline"><semantics><msub><mi mathvariant="double-struck">F</mi><msup><mi>p</mi><mi>m</mi></msup></msub></semantics></math></inline-formula>, and let <inline-formula><math display="inline"><semantics><mrow><mi mathvariant="script">R</mi><mo>=</mo><mrow><msub><mi mathvariant="double-struck">F</mi><msup><mi>p</mi><mi>m</mi></msup></msub><mrow><mo>[</mo><mi>u</mi><mo>]</mo></mrow></mrow><mo>/</mo><mrow><mo stretchy="false">⟨</mo><msup><mi>u</mi><mn>3</mn></msup><mo stretchy="false">⟩</mo></mrow></mrow></semantics></math></inline-formula> be the finite commutative chain ring. In this paper, the symbol-pair distances of all <inline-formula><math display="inline"><semantics><mi>γ</mi></semantics></math></inline-formula>-constacyclic codes of length <inline-formula><math display="inline"><semantics><msup><mi>p</mi><mi>s</mi></msup></semantics></math></inline-formula> over <inline-formula><math display="inline"><semantics><mi mathvariant="script">R</mi></semantics></math></inline-formula> are completely determined.
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