ISSN:

1930-5346

eISSN:

1930-5338

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## Advances in Mathematics of Communications

February 2018 , Volume 12 , Issue 1

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**Abstract:**

Recently, several classes of cyclic codes with three nonzero weights were constructed. With the generic construction presented by C. Ding, T. Helleseth, T. Kløve and X. Wang, we present new systematic authentication codes based on these cyclic codes. In this paper, we study three special classes of cyclic codes and their authentication codes. With the help of exponential sums, we calculate the maximum success probabilities of the impersonation and substitution attacks on the authentication codes. Our results show that these new authentication codes are better than some of the authentication codes in the literature. As a byproduct, the number of times that each element occurs as the coordinates in the codewords of the cyclic codes is settled, which is a difficult problem in general.

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**Abstract:**

The problem of private set-intersection (PSI) has been traditionally treated as an instance of the more general problem of multi-party computation (MPC). Consequently, in order to argue security, or compose these protocols one has to rely on the general theory that was developed for the purpose of MPC. The pursuit of efficient protocols, however, has resulted in designs that exploit properties pertaining to PSI. In almost all practical applications where a PSI protocol is deployed, it is expected to be executed *multiple* times, possibly on related inputs. In this work we initiate a dedicated study of PSI in the multi-interaction (MI) setting. In this model a server sets up the common system parameters and executes set-intersection multiple times with potentially different clients. We discuss a few attacks that arise when protocols are naïvely composed in this manner and, accordingly, craft security definitions for the MI setting and study their inter-relation. Finally, we suggest a set of protocols that are MI-secure, at the same time almost as efficient as their parent, stand-alone, protocols.

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**Abstract:**

Combinatorial batch codes were defined by Paterson, Stinson, and Wei as purely combinatorial versions of the batch codes introduced by Ishai, Kushilevitz, Ostrovsky, and Sahai. There are

In this paper, we investigate erasure batch codes with

*+*[Abstract](1476)

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**Abstract:**

In practice, when a frequency-hopping sequence (FHS) set is applied in a frequency-hopping multiple-access (FHMA) system, its periodic partial Hamming correlation (PPHC) rather than its periodic Hamming correlation (PHC) within the whole period is used to evaluate the system performance. Moreover, FHS sets with low hit zone (LHZ) can be well applied in quasi-synchronous (QS) FHMA systems in which some relative time delay among different users within a zone around the origin can be allowed. Therefore, it is very urgent to conduct research on LHZ FHS sets with optimal PPHC property in depth. In this paper, we first derive a new tighter lower bound on the maximum PPHC of an LHZ FHS set. Then we present a new class of optimal one-coincidence FHS sets. Finally we have a construction of LHZ FHS sets which can be optimal with respect to our new lower bound.

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**Abstract:**

Power decoding, or "decoding using virtual interleaving" is a technique for decoding Reed-Solomon codes up to the Sudan radius. Since the method's inception, it has been an open question if it is possible to use this approach to decode up to the Johnson radius - the decoding radius of the Guruswami-Sudan algorithm. In this paper we show that this can be done by incorporating a notion of multiplicities. As the original Power decoding, the proposed algorithm is a one-pass algorithm: decoding follows immediately from solving a shift-register type equation, which we show can be done in quasi-linear time. It is a "partial bounded-distance decoding algorithm" since it will fail to return a codeword for a few error patterns within its decoding radius; we investigate its failure behaviour theoretically as well as give simulation results.

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**Abstract:**

Shiromoto (Linear Algebra Applic 295 (1999) 191-200) obtained the basic exact sequence for the Lee and Euclidean weights of linear codes over

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**Abstract:**

While analyzing

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Irreducible constacyclic codes constitute an important family of error-correcting codesand have applications in space communications.In this paper, we provide a trace description of irreducible constacyclic codes of length

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**Abstract:**

Motivated by previous computations in Garcia, Stichtenoth and Xing (2000) paper [

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**Abstract:**

We introduce the Multilevel Erasure Channel (MEC) for binary extension field alphabets. The channel model is motivated by applications such as non-volatile multilevel read storage channels. Like the recently proposed

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**Abstract:**

A

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**Abstract:**

We present a new family of one-coincidence sequence sets suitable for frequency hopping code division multiple access (FH-CDMA) systems with dispersed (low density) sequence elements. These sets are derived from one-coincidence prime sequence sets, such that for each one-coincidence prime sequence set there is a new one-coincidence set comprised of sequences with dispersed sequence elements, required in some circumstances, for FH-CDMA systems. Getting rid of crowdedness of sequence elements is achieved by doubling the size of the sequence element alphabet. In addition, this doubling process eases control over the distance between adjacent sequence elements. Properties of the new sets are discussed.

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**Abstract:**

We study complementary information set codes of length

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**Abstract:**

In this paper, we discuss a point about applying known decomposition techniques in their most general form. Three versions of these methods, which are useful for obtaining upper bounds on the optimal information ratios of access structures, are known as: Stinson's $λ$-decomposition, $(λ, ω)$-decomposition and $λ$-weighted-decomposition, where the latter two are generalizations of the first one. We continue by considering the problem of determining the exact values of the optimal information ratios of the reduced access structures with exactly four minimal qualified subsets on six participants, which remained unsolved in Martí-Farré et al.'s paper [Des. Codes Cryptogr. 61 (2011), 167-186]. We improve the known upper bounds for all the access structures, except four cases, determining the exact values of the optimal information ratios. All three decomposition techniques are used while some cases are handled by taking full advantage of the generality of decompositions.

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**Abstract:**

Finite length sequences with large nonlinear complexity over

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