Deletion correction codes have been used for transmission synchronization and, more recently, tracing pirated media. A generalized Reed-Solomon (GRS) code, denoted by GRSk(l,q,alpha,v), is a code of length l over GF(q) with qk codewords. These codes have an efficient decoding algorithm and have been widely used for error correction and detection. It was recently demonstrated that GRS codes are ...

The number of correctable errors of weight half the minimum distance is given for the first-order binary Reed-Muller codes. It is shown that the size of trial set, which is introduced by Helleseth et al. and can be used for a minimum distance decoding or estimating the number of uncorrectable errors, for the first-order Reed-Muller codes is at least that of minimal codewords except for small code

In error-correcting codes for combating noisy transmission channels, a central concept i s the notion of minimum distance. If a code can be constructed with minimum distance between code points of 2m-k 1 I then any number of errors per code word which does not exceed m can be corrected, thus increasing the reliability of transmission above that to be expected with no redundancy i n the code. An...

t immaru-A q-nary error-correcting code with N = qk code words of length n = k + r can have no greater miniium distance d than r + 1. The class of codes for which d = r + 1 is studied first in general, then with the restriction that the codes be linear. Examples and construction methods are given to show that these codes exist for a number of values of q, k, and r. Proof: Pick any k position. T...

We construct error-correcting (nonlinear) binary codes using a construction of Bose and Chowla in additive number theory. Our method extends a construction of Graham and Sloane for constant weight codes. The new codes improve 1028 of the 7168 best known h-error correcting codes of wordlength ≤ 512 with 1 ≤ h ≤ 14. We give asymptotical comparisons to shortened BCH codes.

A serially concatenated code with interleaver consists of the cascade of an outer encoder, an interleaver permuting the outer codeword bits, and an inner encoder whose input words are the permuted outer codewords. In this paper we derive design guidelines for the outer and inner codes that maximize the interleaver gain and the asymptotic slope of the error probability curves.

— To study how to design steganographic algorithm more efficiently, a new coding problem – steganographic codes (abbreviated stego-codes) – is presented in this paper. The stego-codes are defined over the field with q(q ≥ 2) elements. Firstly a method of constructing linear stego-codes is proposed by using the direct sum of vector subspaces. And then the problem of linear stego-codes is convert...

We present families of binary systematic codes that can correct t random errors and detect more than t unidirectional errors. As in recent papers, we start by encoding the k information symbols into a codeword of an [n', k, 2t + 11 error correcting code. The second step of our construction involves adding more bits to this linear error correcting code in order to obtain the detection capability...

A complete classification of the perfect binary oneerror-correcting codes of length 15 as well as their extensions of length 16 was recently carried out in [P. R. J. Östergård and O. Pottonen, “The perfect binary one-error-correcting codes of length 15: Part I—Classification,” submitted for publication]. In the current accompanying work, the classified codes are studied in great detail, and the...

In digital communication, convolutional codes are important to control the errors between the transmitter and receiver. Convolutional code is a type of error correction code (ECC) which can perform both error detection and correction operation between transmitter and receiver side. Here information bits are transformed serially through the architecture which is one of the major advantages as co...