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- W2586312577 abstract "Let p be a prime number and K be the finite field of p elements, i.e. K=GF(p). Further let G be an elementary abelian p-group of order pm. Then the group algebra K[G] is modular. We consider K[G] as an ambient space and the ideals of K[G] as linear codes. A basis of a linear space is called visible, if there exists a member of the basis with the minimum (Hamming) weight of the space. The group algebra approach enables us to find some linear codes with a visible basis in the Jacobson radical of K[G]. These codes can be generated by “monomials” (Drensky & Lakatos, 1989). For p>2, some of our monomial codes have better parameters than the Generalized Reed–Muller codes. In the last part of the paper we determine the automorphism groups of some of the introduced codes." @default.
- W2586312577 created "2017-02-17" @default.
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- W2586312577 date "2017-05-01" @default.
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- W2586312577 title "On monomial codes in modular group algebras" @default.
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- W2586312577 doi "https://doi.org/10.1016/j.disc.2016.12.014" @default.
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