| Summary: | Motivated by the application of high-density data storage technologies, Cassuto and Blaum introduced codes for symbol-pair read channels in 2011, and Yaakobi et al. generalized the coding framework to that for <i>b</i>-symbol read channels where <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>b</mi><mo>≥</mo><mn>2</mn></mrow></semantics></math></inline-formula> in 2016. In this paper, we establish a <i>b</i>-sphere-packing bound and present a recurrence relationship for the <i>b</i>-weight enumerator. We determine all parameters of linear perfect <i>b</i>-symbol <i>e</i>-error-correcting codes over <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> for <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>e</mi><mo><</mo><mn>2</mn><mi>b</mi></mrow></semantics></math></inline-formula> and show that for <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>2</mn><mi>b</mi><mo>≤</mo><mi>e</mi><mo><</mo><mn>3</mn><mi>b</mi></mrow></semantics></math></inline-formula>, there exist at most finite such codes for a given <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>b</mi><mo>,</mo><mo> </mo><mi>e</mi><mo>,</mo></mrow></semantics></math></inline-formula> and <i>q</i>. We construct a family of linear perfect <i>b</i>-symbol <i>b</i>-error-correcting codes over <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> using constacyclic codes.
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