Binary sequences are widely used in various practical fields, such as telecommunications, radar technology, navigation, cryptography, measurement sciences, biology or industry. In this letter, a method to generate long binary sequences (LBS) with low peak sidelobe level (PSL) value is proposed. Having an LBS with length n, both the time and memory complexities of the proposed algorithm are O(n). During our experiments, we repeatedly reach better PSL values than the currently known state of art constructions, such as Legendre sequences, with or without rotations, Rudin-Shapiro sequences or m-sequences, with or without rotations, by always reaching a record-breaking PSL values strictly less than √n. Furthermore, the efficiency and simplicity of the proposed method are particularly beneficial to the lightweightness of the implementation, which allowed us to reach record-breaking PSL values for less than a second.

Simple and efficient algorithm based on heuristic search by shotgun hill climbing to construct binary sequences with small peak sidelobe levels (PSL) is suggested. The algorithm is applied for generation of binary sequences of lengths between 106 and 300. Improvements are obtained in almost half of the considered lengths while for the rest of the lengths, binary sequences with the same PSL values as reported in the state-of-the-art publications are found.

All binary polynomials of degree up to 10 which are suitable to be used as generator polynomials of CRC codes are classified and all the necessary data for the evaluation of the error control performance of the CRC codes generated by the classified polynomials is calculated. A procedure, based on the computed data, for choosing the best CRC code is suggested.

The aim of this work is a systematic investigation of the possible parameters of quasi-perfect (QP) binary and ternary linear codes of small dimensions and preparing a complete classification of all such codes. First, we give a list of infinite families of QP codes which includes all binary, ternary, and quaternary codes known to us. We continue further with a list of sporadic examples of binary and ternary QP codes. Later we present the results of our investigation where binary QP codes of dimensions up to 14 and ternary QP codes of dimensions up to 13 are classified.

Using classification of codes with a certain covering radius it is proved that the least covering radius t[17,6]=5; t[17,8]=4; t[18,7]=5; t[19,7]=5; t[20,8]=5; and t[21,7]=6. As a corollary, four improvements on the length function l(m,R) are found. It is also shown that there exists a unique[14,6] code with covering radius 3.

We investigate the weight structure and error-correcting performance of the ternary [13, 7, 5] quadratic-residue code. It is shown that the covering radius of the code is equal to three and it is t-proper for error correction for any t=0, 1, 2. Two decoding algorithms are suggested.

The covering radius of all ternary negacyclic codes of even length up to 26 is given. The minimum distances and weight distributions of all codes were recalculated. Seven of the open cases for the least covering radius of ternary linear codes were solved and for the other three cases upper bounds were improved.

The maximum number of codewords in a binary code with length n and minimum distance d is denoted by A(n, d). By construction it is known that A(10, 3)/spl ges/72 and A(11, 3)/spl ges/144. These bounds have long been conjectured to be the exact values. This is here proved by classifying various codes of smaller length and lengthening these using backtracking and isomorphism rejection. There are 562 inequivalent codes attaining A(10, 3)=72 and 7398 inequivalent codes attaining A(11, 3)=144.

The covering radii and the least covering radii of all two- and three-dimensional codes over GF(3) are given in the present work. The exact values of the least covering radii of some ternary linear codes of codimensions up to 8 are also determined, and a table of values of t/sub 3/[n,k] for n/spl les/27 is presented.