منابع مشابه
Computation of Minimum Hamming Weight for Linear Codes
In this paper, we consider the minimum Hamming weight for linear codes over special finite quasi-Frobenius rings. Furthermore, we obtain minimal free $R$-submodules of a finite quasi-Frobenius ring $R$ which contain a linear code and derive the relation between their minimum Hamming weights. Finally, we suggest an algorithm that computes this weight using the Grobner basis and we show that und...
متن کاملSemigroup Rings and the Extension Theorem for Linear Codes
An extension theorem for general weight functions is proved over nite commutative local principal ideal rings. The structure of the complex semigroup ring associated to the multiplicative semigroup of the ring plays a prominent role in the proof. 1. Background In her doctoral dissertation, MacWilliams [8], [9] proved an equivalence theorem: two linear codes C1; C2 F n de ned over a nite eld F a...
متن کاملAn Assmus-Mattson theorem for Z4-codes
The Assmus{Mattson theorem is a method to nd designs in linear codes over a nite eld. The purpose of this paper is to give an analogue of this theorem for Z 4 -codes by using the harmonic weight enumerator which is introduced by Bachoc. This theorem can nd some 5-designs in the lifted Golay code over Z 4 which were discovered previously by other methods. Index Terms { Z 4 -codes, Assmus{Mattson...
متن کاملContemporary Mathematics Weight Functions and the Extension Theorem for Linear Codes over Finite Rings
An extension theorem for general weight functions is proved over nite chain rings. The structure of the complex semigroup ring associated to the multiplicative semigroup of the ring plays a prominent role in the proof.
متن کاملLinear constructions for DNA codes
In this paper we translate in terms of coding theory constraints that are used in designingDNAcodes for use in DNA computing or as bar-codes in chemical libraries. We propose new constructions for DNA codes satisfying either a reverse-complement constraint, a GC-content constraint, or both, that are derived from additive and linear codes over four-letter alphabets. We focus in particular on cod...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Finite Fields and Their Applications
سال: 2017
ISSN: 1071-5797
DOI: 10.1016/j.ffa.2017.03.011