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Advances in Mathematics of Communications (AMC) publishes original research papers of the highest quality in all areas of mathematics and computer science which are relevant to applications in communications technology. For this reason, submissions from many areas of mathematics are invited, provided these show a high level of originality, new techniques, an innovative approach, novel methodologies, or otherwise a high level of depth and sophistication. Any work that does not
conform to these standards will be rejected.
Areas covered include coding theory, cryptology, combinatorics, finite geometry, algebra and number theory, but are not restricted to these. This journal also aims to cover the algorithmic and computational aspects of these disciplines. Hence, all mathematics and computer science contributions of appropriate depth and relevance to the above mentioned applications in communications technology are welcome.
More detailed indication of the journal's scope is given by the subject interests of the members of the board of editors.
All papers will undergo a thorough peer reviewing process unless the subject matter of the paper does not fit the journal; in this case, the author will be informed promptly. Every effort will be made to secure a decision in three months and to publish accepted papers within six months.
AMC publishes four issues in 2017 in February, May, August and November and is a joint publication of the American Institute of Mathematical Sciences and Shandong University.
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TOP 10 Most Read Articles in AMC, February 2017
1 
Zero correlation zone sequence set with intergroup orthogonal and intersubgroup complementary properties
Volume 9, Number 1, Pages: 9  21, 2015
Zhenyu Zhang,
Lijia Ge,
Fanxin Zeng
and Guixin Xuan
Abstract
References
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In this paper, a novel method for constructing complementary
sequence set with zero correlation zone (ZCZ) is presented by
interleaving and combining three orthogonal matrices. The
constructed set can be divided into multiple sequence groups and
each sequence group can be further divided into multiple sequence
subgroups. In addition to ZCZ properties of sequences from the same
sequence subgroup, sequences from different sequence groups are
orthogonal to each other while sequences from different sequence
subgroups within the same sequence group possess ideal
crosscorrelation properties, that is, the proposed ZCZ sequence set
has intergroup orthogonal (IGO) and intersubgroup complementary
(ISC) properties. Compared with previous methods, the new
construction can provide flexible choice for ZCZ width and set size,
and the resultant sequences which are called IGOISC sequences in
this paper can achieve the theoretical bound on the set size for the
ZCZ width and sequence length.

2 
Bent functions on a Galois ring and systematic authentication codes
Volume 6, Number 2, Pages: 249  258, 2012
Claude Carlet,
Juan Carlos KuCauich
and Horacio TapiaRecillas
Abstract
References
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A class of bent functions on a Galois ring is introduced and based on these functions systematic authentication codes are presented. These codes generalize those appearing in [4] for finite fields.

3 
Generalized AG convolutional codes
Volume 3, Number 4, Pages: 317  328, 2009
José Ignacio Iglesias Curto
Abstract
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We present the family of generalized AG convolutional codes, constructed
by using algebraic geometric tools. This construction extends block
generalized AG codes on the one hand and several algebraic constructions of
convolutional codes on the other. The tools employed to define these codes
are also used to obtain information about their parameters and to determine
conditions such that the resulting codes have optimal free distance.

4 
On weighted minihypers in finite projective spaces of square order
Volume 9, Number 3, Pages: 291  309, 2015
Linda Beukemann,
Klaus Metsch
and Leo Storme
Abstract
References
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In [11], weighted $\{\delta(q+1),\delta;k1,q\}$minihypers, $q$ square, were characterized as a sum of lines and Baer subgeometries $PG(3,\sqrt{q})$ provided $\delta$ is sufficiently small. We extend this result to a new characterization result on weighted $\{\delta v_{\mu+1},\delta v_{\mu};k1,q\}$minihypers. We prove that such minihypers are sums of $\mu$dimensional subspaces and of (projected) $(2\mu+1)$dimensional Baer subgeometries.

5 
Weight distributions of a class of cyclic codes from $\Bbb F_l$conjugates
Volume 9, Number 3, Pages: 341  352, 2015
Chengju Li,
Qin Yue
and Ziling Heng
Abstract
References
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Let $\Bbb F_{q^k}$ be a finite field and $\alpha$ a primitive element of $\Bbb F_{q^k}$, where $q=l^f$,
$l$ is a prime power, and $f$ is a positive integer.
Suppose that $N$ is a positive integer and $m_{g^{l^u}}(x)$ is the minimal polynomial of $g^{l^u}$ over $\Bbb F_q$
for $u=0, 1, \ldots, f1$, where $g=\alpha^{N}$.
Let $\mathcal C$ be a cyclic code over $\Bbb F_q$ with check polynomial $$m_g(x)m_{g^l}(x) \cdots m_{g^{l^{f1}}}(x).$$
In this paper, we shall present a method to determine the weight distribution of the cyclic code $\mathcal C$ in two cases: (1) $\gcd(\frac {q^k1} {l1}, N)=1$; (2) $l=2$ and $f=2$.
Moreover, we will obtain a class of twoweight cyclic codes and a class of new threeweight cyclic codes.

6 
Highrate spacetime block codes from twisted Laurent series rings
Volume 9, Number 3, Pages: 255  275, 2015
Hassan Khodaiemehr
and Dariush Kiani
Abstract
References
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We construct fulldiversity, arbitrary rate STBCs for specific number of transmit
antennas over an apriori specified signal set using twisted Laurent series rings. Constructing fulldiversity spacetime block codes from algebraic constructions like division algebras
has been done by Shashidhar et al. Constructing STBCs from crossed product algebras arises this question in mind that besides these constructions, which one of the wellknown division algebras are appropriate for constructing spacetime block codes.
This paper deals with twisted Laurent series rings and their subrings twisted function fields, to construct STBCs. First, we introduce twisted Laurent series rings over field extensions of $\mathbb{Q}$. Then, we generalize this construction to the case that coefficients come from a division algebra.
Finally, we use an algorithm to construct twisted function fields, which are noncrossed product division algebras, and we propose a method for constructing STBC from them.

7 
Ideal forms of Coppersmith's theorem and GuruswamiSudan list decoding
Volume 9, Number 3, Pages: 311  339, 2015
Henry Cohn
and Nadia Heninger
Abstract
References
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We develop a framework for solving polynomial equations with size
constraints on solutions. We obtain our results by showing how to apply a
technique of Coppersmith for finding small solutions of polynomial
equations modulo integers to analogous problems over polynomial rings,
number fields, and function fields. This gives us a unified view of several
problems arising naturally in cryptography, coding theory, and the study of
lattices. We give (1) a polynomialtime algorithm for finding small
solutions of polynomial equations modulo ideals over algebraic number
fields, (2) a faster variant of the GuruswamiSudan algorithm for list
decoding of ReedSolomon codes, and (3) an algorithm for list decoding of
algebraicgeometric codes that handles both singlepoint and multipoint
codes. Coppersmith's algorithm uses lattice basis reduction to find a
short vector in a carefully constructed lattice; powerful analogies from
algebraic number theory allow us to identify the appropriate analogue of a
lattice in each application and provide efficient algorithms to find a
suitably short vector, thus allowing us to give completely parallel proofs
of the above theorems.

8 
The weight distributions of some irreducible cyclic codes of length $p^n$ and $2p^n$
Volume 9, Number 3, Pages: 277  289, 2015
Pankaj Kumar,
Monika Sangwan
and Suresh Kumar Arora
Abstract
References
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In this paper, an algorithm is given for computing the weight distributions of all irreducible cyclic
codes of dimension $p^jd$ generated by $x^{p^j}1$, where $p$ is an
odd prime, $j\geq 0 $ and $d > 1$. Then the weight distributions of
all irreducible cyclic codes of length $p^n$ and $ 2p^n $ over
$F_q$, where $n$ is a positive integer, $p$, $q$ are distinct odd
primes and $q$ is primitive root modulo $ p^n$, are obtained. The
weight distributions of all the irreducible cyclic codes of length
$3^{n+1}$ over $F_5$ are also determined explicitly.

9 
GilbertVarshamov type bounds for linear codes over finite chain rings
Volume 1, Number 1, Pages: 99  109, 2007
Ferruh Özbudak
and Patrick Solé
Abstract
Full Text
Related Articles
We obtain finite and asymptotic GilbertVarshamov type bounds
for linear codes over finite chain rings with various weights.

10 
Gold and KasamiWelch functions, quadratic forms, and bent functions
Volume 1, Number 2, Pages: 243  250, 2007
Jyrki Lahtonen,
Gary McGuire
and Harold N. Ward
Abstract
Full Text
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We use elementary facts about quadratic forms in characteristic
2 to evaluate the sign of some Walsh transforms in terms of a Jacobi symbol. These results are applied to the Walsh transforms of the Gold and KasamiWelch functions. We prove that the Gold functions yield bent functions when restricted to certain hyperplanes. We also use the sign information to determine the dual bent function.

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