Abstract: This paper studies linear codes capable of detecting and correcting solid burst error of length b or less. The lower and upper bounds on the number of parity-check digits required for such codes are obtained. Illustrations of codes for detecting as well as correcting such errors are provided.

Abstract: The Schmidt–Sidorenko–Bossert scheme extends a low-rate Reed–Solomon code to an Interleaved Reed–Solomon code and achieves the decoding radius of Sudan’s original list decoding algorithm while the decoding result remains unambiguous. We adapt this result to the case of Generalized Reed–Solomon codes and calculate the parameters of the corresponding Interleaved Generalized Reed–Solomon code. Furthermore, the failure probability is derived.

Abstract: In this paper, we study linear codes capable of detecting and correcting s-periodic errors. Lower and upper bounds on the number of parity check digits required for codes detecting such errors are obtained. Another bound on codes correcting such errors is also obtained. An example of a code detecting such errors is provided.

Abstract: It is shown that interleaved Reed-Solomon codes can be list-decoded for burst errors while attaining the generalized Reiger bound for list decoding.

Abstract: The letter presents binary cyclic codes with the maximum burst error correction capability. This is achieved based on the properties of circulant parity check matrix. Results conclude existence of codes with high minimum weight and rate greater than 0.28. It also gives cyclic product codes suitable for multiple burst and random error corrections.

Abstract: Two-dimensional product code has been studied for correcting burst errors on the storage systems. An RS-LDPC product code consists of an RS code in horizontal direction and an LDPC code in vertical direction. First, we detect the position of burst errors by using RS code, then LDPC code corrects the errors by using the burst error positions. In storage system, long burst errors are occurred by various reason. So, we need a strong code for correcting the long burst errors. RS-LDPC product code is good for long burst errors. However, as the storage density grows the length of the burst errors will be longer. Thus, we propose an LDPC-LDPC product code, it is strong for correcting the very long burst errors. Also, the proposed LDPC-LDPC product code performs better than RS-LDPC product code when the random errors are occurred, because a row direction LDPC code performs better than row direction RS code.

Abstract: This paper presents lower bound on the number of parity-check digits required for linear codes that correct m-repeated low-density burst errors of length b (fixed) with weight w or less (w ≤ b). An upper bound on the number of parity-check digits required for linear codes that are capable of detecting such m-repeated low-density bursts has also been derived.

Abstract: We introduce a technique for constructing codes for bursts of errors that have some known structure; for example bursts of length at most b and Hamming weight at most t. This technique is based on modifying existing codes for generic bursts by replacing a portion of their check matrix with a more efficient one, in light of the additional constraints on the burst. We illustrate this procedure by modifying the Fire, Burton and Gilbert codes to address bursts with maximum Hamming weight, bursts with solid errors, or bursts with internal “mini-bursts”. We provide evidence that the redundancy of the codes we construct can be very good through examples, one of which is optimal within the class of cyclic codes.

Abstract: The Lee weight is more appropriate for some practical situations than the Hamming weight as it takes into account of the magnitude of each digit of the word. In this paper, we obtain a sufficient condition over the number of parity check digits for codes correcting simultaneously random and burst errors with Lee weight consideration. This sufficient condition is an extension of the Varshamov-Gilbert-Sacks bound for codes correcting simultaneously random and burst errors with Lee weight constraint.

Abstract: Cyclic codes give us the most probable method by which we may detect and correct data transmission errors. These codes depend on the development of advanced mathematical concepts. It is shown that cyclic codes when viewed as vector subspaces of a vector space of some dimension n over some finite field F can be approached as polynomials in a ring. This approach is made possible by the assumption that the set of codewords is invariant under cyclic shifts which are linear transformations. Developing these codes seems to be equivalent to factoring the polynomial x[superscript]n-x over F. Each factor then gives us a cyclic code of some dimension k over F. Constructing factorizations of x[superscript]n-x is accomplished by using cyclotomic polynomials and idempotents of the code algebra. The use of these two concepts together allows us to find cyclic codes in F[superscript]n. Hence the development of cyclic codes is a journey from codewords and codes to fields and rings and back to codes and codewords.

Abstract: The paper contains a report on Simulation of the Burst Error Correction. Most of the practical communica- tion channels such as magnetic storage systems, telephone lines, optical discs used to store digital data such as CD,DVD etc are affected by errors which are concentrated in a certain locality rather than randoms errors. These errors may be due to physical damage such as scratch on a disc or a stroke of lightning in case of wireless channel. Such errors occur in a burst (called as burst because they are occurring in many consecutive bits). The methods used to correct random errors are inefficient to correct such burst errors. This motivates burst error correcting codes. The idea of interleaving is used to convert convolutional codes used to random error correction for burst error correction. During the message transmission, an impairment occurs from time to time i.e. an error arises which is caused by interfering signals during the transmission. The situation requires that the respective coding is adapted as much as possible to the given conditions of the transmission. The convolutional coding is suitable for the correction of burst errors. However, the procedure of the majority of burst error correction solutions is very demanding. This article therefore explains a complex procedure of design and simulation in Matlab on a specific case which is suitable for its simplicity and makes the explanation of the lesson easier. The algorithm principle is based on the detection of the shortest Hamming distance of the decoded sequence from the received sequence. The substantial disadvantage of the above-mentioned method consists in the fact that it is significantly demanding as for the number of numerical operations. This method is used only for the decoding of codes with relatively short constraint lengths because the dependency of the number of operations on the constraint length has an exponential character. Another method which can be used for error detection is the threshold decoding principle. The threshold decoding is based on finding a sufficient number of check operations among the elements of message sections which are in the so-called orthogonality rela- tion towards the element whose correctness is checked after the transmission. The latter method shall be outlined in this docu-

Abstract: The purpose of this paper is to propose a simple method of constructing a parity-check matrix for any binary linear code capable of correcting a new kind of burst error called 'm-repeated burst error of length b or less' recently introduced by the authors. Some binary codes based on the proposed technique have been illustrated. This technique for m = 1 helps in resolving a long standing problem of devising a systematic algorithm for the construction of a burst error correcting code.

Abstract: In this paper, we obtain lower and upper bounds for linear codes which are capable of correcting the errors blockwise that occur during the process of transmission. The kinds of errors considered are known as s-periodic errors. Illustrations for such kind of codes have also been provided.

Abstract: Cyclic codes with two zeros and their dual codes as a practically and theoretically interesting class of linear codes have been studied for many years and find many applications. The determination of the weight distributions of such codes is an open problem. Generally, the weight distributions of cyclic codes are difficult to determine. Utilizing a class of elliptic curves, this paper determines the weight distributions of dual codes of q-ary cyclic codes with two zeros for a few more cases, where q is an odd prime power.