Although steganographic transparency and embedding capacity are considered to be two conflicting objectives in the design of steganographic systems, it is possible and necessary to strike a good balance between them i...
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Although steganographic transparency and embedding capacity are considered to be two conflicting objectives in the design of steganographic systems, it is possible and necessary to strike a good balance between them in Voice-over-IP steganography. In this paper, to improve steganographic transparency while maintaining relatively large embedding capacity, the authors present a (2n-1, 2n) covering code, which can hide 2n-1 bits of secret messages into 2n bits of cover messages with not more than n-bit changed. Specifically, each (2n-1)-bit secret message is first transformed into two 2n-bit candidate codewords. In embedding process, the cover message is replaced with the optimal codeword more similar with it. In this way, the embedding distortion can be largely reduced. The proposed method is evaluated by comparing with existing ones with a large number of ITU-T G. 729a encoded speech samples. The experimental results show that the authors' scheme can provide good performance on both steganographic transparency and embedding capacity, and achieve better balance between the two objectives than the existing ones.
Linear codes with few weights have wide applications in consumer electronics, data storage system and secret sharing. In this paper, by virtue of planar functions, several infinite families of l-weight linear codes ov...
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Linear codes with few weights have wide applications in consumer electronics, data storage system and secret sharing. In this paper, by virtue of planar functions, several infinite families of l-weight linear codes over F p are constructed, where l can be any positive integer and p is a prime number. The weight distributions of these codes are determined completely by utilizing certain approach on exponential sums. Experiments show that some (almost) optimal codes in small dimensions can be produced from our results. Moreover, the related covering codes are also investigated. (c) 2024 Published by Elsevier Inc.
The minimum size of a binary covering code of length n and covering radius r is denoted by K(n, r), and codes of this length are called optimal. For j > 0 and n = 2(j), it is known that K(n, 1) = 2 (.) K(n - 1, 1) ...
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The minimum size of a binary covering code of length n and covering radius r is denoted by K(n, r), and codes of this length are called optimal. For j > 0 and n = 2(j), it is known that K(n, 1) = 2 (.) K(n - 1, 1) = 2(n-j). Say that two binary words of length n form a duo if the Hamming distance between them is 1 or 2. In this paper, it is shown that each optimal binary covering code of length n = 2(j), j > 0, and covering radius 1 is the union of duos in just one way, and that the closed neighborhoods of the duos form a tiling of the set of binary words of length n. Methods of constructing such optimal codes from optimal covering codes of length n - 1 (that is, perfect single-error-correcting codes) are discussed. The paper ends with the construction of an optimal covering code of length 16 that does not contain an extension of any optimal covering code of length 15. (c) 2005 Wiley Periodicals, Inc.
Let K(q)(n,R) denote the minimum number of codewords in any q-ary code of length n and covering radius R. We collect lower and upper bounds for K(q)(n,R) where 6 = 11, we consider n <= 8. This extends earlier resul...
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Let K(q)(n,R) denote the minimum number of codewords in any q-ary code of length n and covering radius R. We collect lower and upper bounds for K(q)(n,R) where 6 <= q <= 21 and R <= 3. For q <= 10, we consider lengths n <= 10, and for q >= 11, we consider n <= 8. This extends earlier results, which have been tabulated for 2 <= q <= 5. We survey known bounds and obtain some new results as well, also for s-surjective codes, which are closely related to covering codes and utilized in some of the constructions.
Lower bounds for K(n,R), the minimal number of codewords of any binary code of length n and covering radius R, are improved. The definition of multiexcess is introduced. A technique combining van Wee's method and ...
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Lower bounds for K(n,R), the minimal number of codewords of any binary code of length n and covering radius R, are improved. The definition of multiexcess is introduced. A technique combining van Wee's method and linear inequalities for covering codes is used. A revised table for K(n,R) (n less-than-or-equal-to 33, R less-than-or-equal-to 10) is given.
Minimal linear codes are in one-to-one correspondence with special types of blocking sets of projective spaces over a finite field, which are called strong or cutting blocking sets. Minimal linear codes have been stud...
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Minimal linear codes are in one-to-one correspondence with special types of blocking sets of projective spaces over a finite field, which are called strong or cutting blocking sets. Minimal linear codes have been studied since decades but their tight connection with cutting blocking sets of finite projective spaces was unfolded only in the past few years, and it has not been fully exploited yet. In this paper we apply finite geometric and probabilistic arguments to contribute to the field of minimal codes. We prove an upper bound on the minimal length of minimal codes of dimension k over the q-element Galois field which is linear in both q and k, hence improve the previous superlinear bounds. This result determines the minimal length up to a small constant factor. We also improve the lower and upper bounds on the size of so called higgledy-piggledy line sets in projective spaces and apply these results to present improved bounds on the size of covering codes and saturating sets in projective spaces as well.
A partial-sum query obtains the summation over a set of specified cells of a data cube. We establish a connection between the covering problem in the theory of error-correcting codes and the partial-sum problem and us...
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A partial-sum query obtains the summation over a set of specified cells of a data cube. We establish a connection between the covering problem in the theory of error-correcting codes and the partial-sum problem and use this connection to devise algorithms for the partial-sum problem with efficient space-time-trade-offs. For example,using our algorithms, with 44 percent additional storage, the query response time can be improved by about 12 percent;by roughly doubling the storage requirement, the query response time can be improved by about 34 percent.
We develop two methods for obtaining new lower bounds for the cardinality of covering codes. Both are based on the notion of linear inequality of a code. Indeed, every linear inequality of a code (defined on F-q(n)) a...
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We develop two methods for obtaining new lower bounds for the cardinality of covering codes. Both are based on the notion of linear inequality of a code. Indeed, every linear inequality of a code (defined on F-q(n)) allows to obtain, using a classical formula (inequality (2) below), a lower bound on K-q(n, R), the minimum cardinality of a covering code with radius R. We first show how to get new linear inequalities (providing new lower bounds) from old ones. Then, we prove some formulae that improve on the classical formula (2) for linear inequalities of some given types. Applying both methods to all the classical cases of the literature, we improve on nearly 20% of the best lower bounds on K-q(n, R). (C) 2000 Elsevier Science B.V. All rights reserved.
Given a prime power q, c(q)(n, R) denotes the minimum cardinality of a subset H in F-q(n) such that every word in this space differs in at most R coordinates from a multiple of a vector in H. In this work, two new cla...
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Given a prime power q, c(q)(n, R) denotes the minimum cardinality of a subset H in F-q(n) such that every word in this space differs in at most R coordinates from a multiple of a vector in H. In this work, two new classes of short coverings are established. As an application, a new optimal record-breaking result on the classical covering code is obtained by using short covering. We also reformulate the numbers c(q)(n, R) in terms of dominating set on graphs. Departing from this reformulation, the reactive tabu search (a variation of tabu search heuristics) is developed to obtain new upper bounds on c(q)(n, R). The algorithm is described and conclusions on the results are drawn;they identify the advantages of using the reactive mechanism for this problem. Tables of lower and upper bounds on c(q)(n, R), q = 3, 4, n <= 7, and R <= 3, are also presented. (C) 2009 Elsevier B.V. All rights reserved.
Let K(n, r) denote the minimum cardinality of a binary covering code of length n and covering radius r. Constructions of covering codes give upper bounds on K(n, r). It is here shown how computer searches for covering...
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Let K(n, r) denote the minimum cardinality of a binary covering code of length n and covering radius r. Constructions of covering codes give upper bounds on K(n, r). It is here shown how computer searches for covering codes can be sped up by requiring that the code has a given (not necessarily full) automorphism group. Tabu search is used to find orbits of words that lead to a covering. In particular, a code D is found which proves K(13, 1) less than or equal to 704 a new record. A direct construction of D is given, and its full automorphism group is shown to be the general linear group GL(3, 3). It is proved that D is a perfect dominating set (each word not in D is covered by exactly one word in D) and is a counterexample to the recent Uniformity Conjecture of Weichsel.
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