Asymmetric quantum error-correcting codes (AQCs) may offer some advantage over their symmetric counterparts by providing better error-correction for the more frequent error types. The well-known CSS construction of q-ary AQCs is extended by removing the Fq-linearity requirement as well as the limitation on the type of inner product used. The proposed constructions are called CSS-like constructions and utilize pairs of nested subfield linear codes under one of the Euclidean, trace Euclidean, Hermitian, and trace Hermitian inner products.After establishing some theoretical foundations, bestperforming CSS-like AQCs are constructed. Combining some constructions of nested pairs of classical codes and linear programming, many optimal and good pure q-ary CSS-like codes for q ∈ {2, 3, 4, 5, 7, 8, 9} up to reasonable lengths are found. In many instances, removing the Fq-linearity and using alternative inner products give us pure AQCs with improved parameters than relying solely on the standard CSS construction.Index Terms-asymmetric quantum codes, best-known linear codes, Delsarte bound, group character codes, cyclic codes, inner products, linear programming bound, quantum Singleton bound, subfield linear codes I. INTRODUCTIONMost of the work to date on quantum error-correcting codes (quantum codes) assumes that the quantum channel is symmetric, i.e., the different types of errors are assumed to occur equiprobably. However, recent papers (see [13] and [20], for instance) argue that in many qubit systems, phase-flips (or Z-errors) occur more frequently than bit-flips (or X-errors). This leads to the idea of adjusting the error-correction to the particular characteristics of the quantum channel and codes M. F. Ezerman was with

We present a general construction of asymmetric quantum codes based on additive codes under the trace Hermitian inner product. Various families of additive codes over $\F_{4}$ are used in the construction of many asymmetric quantum codes over $\F_{4}$.Comment: Accepted for publication March 2, 2011, IEEE Transactions on Information Theory, to appea

A recent study by one of the authors has demonstrated the importance of profile vectors in DNA-based data storage. We provide exact values and lower bounds on the number of profile vectors for finite values of alphabet size q, read length , and word length n. Consequently, we demonstrate that for q ≥ 2 and n ≤ q /2−1 , the number of profile vectors is at least q κn with κ very close to 1. In addition to enumeration results, we provide a set of efficient encoding and decoding algorithms for each of two particular families of profile vectors.

Code-based cryptography is one of few alternatives supposed to be secure in a post-quantum world. Meanwhile, identity-based identification and signature (IBI/IBS) schemes are two of the most fundamental cryptographic primitives, so several code-based IBI/IBS schemes have been proposed. However, with increasingly profound researches on coding theory, the security reduction and efficiency of such schemes have been invalidated and challenged. In this paper, we construct provably secure IBI/IBS schemes from code assumptions against impersonation under active and concurrent attacks through a provably secure code-based signature technique proposed by Preetha, Vasant and Rangan (PVR signature), and a security enhancement Or-proof technique. We also present the parallel-PVR technique to decrease parameter values while maintaining the standard security level. Compared to other code-based IBI/IBS schemes, our schemes achieve not only preferable public parameter size, private key size, communication cost and signature length due to better parameter choices, but also provably secure.

The weights in MDS codes of length n and dimension k over the finite field GF(q) are studied. Up to some explicit exceptional cases, the MDS codes with parameters given by the MDS conjecture are shown to contain all k weights in the range n-k+1 to n. The proof uses the covering radius of the dual codeComment: 5 pages, submitted to IEEE Trans. IT. This version 2 is the revised version after the refereeing process. Accepted for publicatio

Using the Calderbank-Shor-Steane (CSS) construction, pure q-ary asymmetric quantum error-correcting codes attaining the quantum Singleton bound are constructed. Such codes are called pure CSS asymmetric quantum maximum distance separable (AQMDS) codes. Assuming the validity of the classical MDS Conjecture, pure CSS AQMDS codes of all possible parameters are accounted for.

We solve an open question in code-based cryptography by introducing two provably secure group signature schemes from code-based assumptions. Our basic scheme satisfies the CPA-anonymity and traceability requirements in the random oracle model, assuming the hardness of the McEliece problem, the Learning Parity with Noise problem, and a variant of the Syndrome Decoding problem. The construction produces smaller key and signature sizes than the previous group signature schemes from lattices, as long as the cardinality of the underlying group does not exceed 2 24 , which is roughly comparable to the current population of the Netherlands. We develop the basic scheme further to achieve the strongest anonymity notion, i.e., CCA-anonymity, with a small overhead in terms of efficiency. The feasibility of two proposed schemes is supported by implementation results. Our two schemes are the first in their respective classes of provably secure groups signature schemes. Additionally, the techniques introduced in this work might be of independent interest. These are a new verifiable encryption protocol for the randomized McEliece encryption and a novel approach to design formal security reductions from the Syndrome Decoding problem.Index Terms-code-based group signature, zero-knowledge protocol, McEliece encryption, syndrome decoding. I. INTRODUCTION A. Background and MotivationGroup signature [1] is a fundamental cryptographic primitive with two intriguing features. The first one is anonymity. It allows users of a group to anonymously sign documents on behalf of the whole group. The second one is traceability. There exists a tracing authority that can tie a given signature to the signer's identity should the need arise. These two properties make group signatures highly useful in various

We propose a construction of de Bruijn sequences by the cycle joining method from linear feedback shift registers (LFSRs) with arbitrary characteristic polynomial f (x). We study in detail the cycle structure of the set Ω ( f (x)) that contains all sequences produced by a specific LFSR on distinct inputs and provide a fast way to find a state of each cycle. This leads to an efficient algorithm to find all conjugate pairs between any two cycles, yielding the adjacency graph. The approach is practical to generate a large class of de Bruijn sequences up to order n ≈ 20. Many previously proposed constructions of de Bruijn sequences are shown to be special cases of our construction.Keywords Binary periodic sequence · LFSR · de Bruijn sequence · cycle structure · adjacency graph · cyclotomic number Mathematics Subject Classification (2010) 11B50 · 94A55 · 94A60 1 Introduction A binary de Bruijn sequence of order n has period N = 2 n in which each n-tuple occurs exactly once in each period. There are 2 2 n−1 −n of them [5]. Some of their earliest applications are in communication systems. They are generated in a deterministic way, yet satisfy the randomness criteria in [14, Ch. 5] and are balanced, containing the same number of 1s and 0s. In cryptography, they have been used as a source of pseudo-random numbers and in keysequence generators of stream ciphers [29, Sect. 6.3]. In computational molecular biology, one of the three assembly paradigms in DNA sequencing is the de Bruijn graph assemblers model [31, Box 2]. Some roles of de Bruijn sequences in robust positioning patterns are discussed by Bruckstein et al. in [4]. They have numerous applications, e.g., in robotics,