منابع مشابه
Circulants , Linear Recurrences and Codes
We shall give some intriguing applications of the theory of circulants—the circulant matrices—and that of linear recurrence sequences (LRS). The applications of the former in §2 ranges from a simple derivation of the Blahut theorem to the energy levels of hydrogen atoms in circular hydrocarbons, where the Blahut theorem is to the effect that the Hamming weight of a code is equal to the rank of ...
متن کاملTwo-weight codes and second order recurrences
Cyclic codes of dimension 2 over a finite field are shown to have at most two nonzero weights. This extends a construction of Rao et al (2010) and disproves a conjecture of Schmidt-White (2002). We compute their weight distribution, and give a condition on the roots of their check polynomials for them to be MDS.
متن کاملArithmetic completely regular codes
In this paper, we explore completely regular codes in the Hamming graphs and related graphs. Experimental evidence suggests that many completely regular codes have the property that the eigenvalues of the code are in arithmetic progression. In order to better understand these “arithmetic completely regular codes”, we focus on cartesian products of completely regular codes and products of their ...
متن کاملSecure FSM-based arithmetic codes
Recently, arithmetic coding has attracted the attention of many scholars because of its high compression capability. Accordingly, in this paper, a method that adds secrecy to this well-known source code is proposed. Finite state arithmetic code is used as source code to add security. Its finite state machine characteristic is exploited to insert some random jumps during source coding process. I...
متن کاملEquidistant Arithmetic Codes and Character Sums
A cyclic arithmetic code is a subgroup of Z/(rn − 1)Z, where the weight of a word x is the minimal number of nonzero coefficients in the representation x ≡ ∑n−1 i=0 cir with |ci| < r for all i. A code is called equidistant if all codewords have the same weight. In this paper necessary conditions for the existence of equidistant codes are given. By relating these conditions to character sums on ...
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ژورنال
عنوان ژورنال: Information and Control
سال: 1977
ISSN: 0019-9958
DOI: 10.1016/s0019-9958(77)80001-6