On cyclic codes in incidence rings
2006 ◽
Vol 43
(1)
◽
pp. 69-77
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Keyword(s):
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.
2018 ◽
Vol 11
(07)
◽
pp. 1850090
Keyword(s):
Keyword(s):
2006 ◽
Vol 412
(2-3)
◽
pp. 396-407
◽
2018 ◽
Vol 10
(03)
◽
pp. 1850031
◽
Keyword(s):
2006 ◽
Vol 153
(5)
◽
pp. 581
◽
2017 ◽
Vol 28
(4)
◽
pp. 339-350
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Keyword(s):
2021 ◽
pp. 1-15
Keyword(s):