<p>In this paper, we construct infinite families of quantum codes of prime length derived from cyclic codes via the Calderbank–Shor–Steane (CSS) and Hermitian constructions. Quantum CSS triadic codes over <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\mathbb {F}_q\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi mathvariant="double-struck">F</mi> <mi>q</mi> </msub> </math></EquationSource> </InlineEquation> and quantum Hermitian triadic codes over <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(\mathbb {F}_{q^2}\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi mathvariant="double-struck">F</mi> <msup> <mi>q</mi> <mn>2</mn> </msup> </msub> </math></EquationSource> </InlineEquation> are presented. We analyze the resulting quantum code families under the 3-splitting condition on the defining set, with a particular focus on the cases <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(q = 2\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>q</mi> <mo>=</mo> <mn>2</mn> </mrow> </math></EquationSource> </InlineEquation> and <InlineEquation ID="IEq4"> <EquationSource Format="TEX">\(q = 3\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>q</mi> <mo>=</mo> <mn>3</mn> </mrow> </math></EquationSource> </InlineEquation>. A cube root bound is also established for the minimum odd-like weight in a triadic code. Finally, we present a method for constructing larger quantum codes by extending small 3-splittings of the underlying quantum codes.</p>