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On cyclic codes in incidence rings

2006
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Studia scientiarum mathematicarum Hungarica (Print)
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Cyclic codes are defined as ideals in polynomial quotient rings. We are using a matrix ring construction in a similar way to define classes of codes. It is shown that all cyclic and all linear codes can be embedded as ideals in this construction. A formula for the largest Hamming weight of one-sided ideals in incidence rings is given. It is shown that every incidence ring defined by a directed graph always possesses a principal one-sided ideal that achieves the optimum Hamming weight. It is

doi:10.1556/sscmath.43.2006.1.5
fatcat:dd6qk2pyuzgkbp2lsik4vdvfiy