Low-density parity-check (LDPC) codes provide capacity approaching performances with very long codes in a coherent channel. However, as the block length increases, their performance becomes worse with residual frequency offsets. Residual frequency offsets can be tackled with sub-block decoding and LDPC code-aided phase ambiguity resolution for binary phaseshift keying (BPSK) signals. Sub-block ...

Constructions of protocol sequences for multiple-access collision channel without feedback are given. These constructions are the extensions of those described by A, GyiiriI, and Massey. If the basic code in their constructions, a Reed-Solomon code, is replaced by a BCH code then the resulting protocol sequences have the feature that, for a given sum rate, the ratio of the total user population...

Let Kq(n, w, t, d) be the minimum size of a code over Zq of length n, constant weight w, such that every word with weight t is within Hamming distance d of at least one codeword. In this article, we determine Kq(n, 4, 3, 1) for all n ≥ 4, q = 3, 4 or q = 2m + 1 with m ≥ 2, leaving the only case (q, n) = (3, 5) in doubt. Our construction method is mainly based on the auxiliary designs, H-frames,...

We considered repeated-root cyclic codes whose block length is divisible by the characteristic of the underlying field. Cyclic self dual codes are also the repeated root cyclic codes. It is known about the one-level squaring construction for binary repeated root cyclic codes. In this correspondence, we introduced of two level squaring construction for binary repeated root cyclic codes of length...

For example, CH the family of Hamming code is a family of codes with ni = 2 − 1, ki = 2 − i − 1, di = 3 and R(CH) = 1, δ(CH) = 0. We will mostly work with family of codes from now on. This is necessary as we will study the asymptotic behavior of algorithms for codes, which does not make sense for a fixed code. For example, when we say we say that a decoding algorithm for a code C takes O(n) tim...

A class of one-dimensional convolutional codes will be presented. They are all MDS codes, i. e., have the largest distance among all one-dimensional codes of the same length n and overall constraint length δ. Furthermore, their extended row distances are computed, and they increase with slope n − δ. In certain cases of the algebraic parameters, we will also derive parity check matrices of Vande...

We improve the method in [1] for increasing the finite-lengh performance of polar codes by protecting specific, less reliable symbols with simple outer repetition codes. Decoding of the scheme integrates easily in the known successive decoding algorithms for polar codes. Overall rate and block length remain unchanged, the decoding complexity is at most doubled. A comparison to related methods f...

Abstmt. It is showc that for any block length n which is a multiple of 5, there exists a binary self dual code irr which all weights are divisible by 4, and the minimum weight is asymptotically the same as that given by the Varshamov-Gilbert bound. § 1. Preliminaries Let Fn denote the vector space of all vectors of length II with components from GF(2). The weiglzt of ii vector u = is the number...

Linear complementary-dual (LCD for short) codes are linear codes that intersect with their duals trivially. LCD codes have been used in certain communication systems. It is recently found that LCD codes can be applied in cryptography. This application of LCD codes renewed the interest in the construction of LCD codes having a large minimum distance. MDS codes are optimal in the sense that the m...

Abstract: Z2Z4-additive codes, as a special class of abelian codes, have found a very welcoming place in the recent studies of algebraic coding theory. This family in one hand is similar to binary codes on the other hand is similar to quaternary codes. The structure of Z2Z4additive codes and their duals has been determined lately. In this study we investigate the algebraic structure of Z2Z2s -a...