Monomial codes were recently equipped with partial order relations, a fact that allowed researchers to discover structural properties and efficient algorithm for constructing polar codes. Here, we refine the existing order relations in the particular...
Over binary-input memoryless symmetric (BMS) channels, the performance of polar codes under successive cancellation list (SCL) decoding can approach maximum likelihood (ML) algorithm when the list size L is greater than or equal to
The codewords of a low-density parity-check (LDPC) convolutional code (LDPC-CC) are characterised into structured and non-structured. The number of the structured codewords is dominated by the size of the polynomial syndrome former matrix...
In this work, we explore the relationship between the graded free resolution of some monomial ideals and the Generalized Hamming Weights (GHWs) of binary codes. More precisely, we look for a structure that is smaller than the set of codewords of mini...
The build-up method is a powerful class of propagation rules that generate self-dual codes over finite fields and unitary rings. Recently, it was extended to non-unitary rings of order 4, to generate quasi self-dual codes. In the present paper, we in...
A Dickson near-field is obtained from
The algebraic analysis of linear code parameters reveals deep connections with cryptographic constructions, including the Information Dispersal Algorithms (IDAs) and secret-sharing schemes. In this work, we propose an algebraic method for constructin...
This article presents the performance analysis and comparison of turbo codes for several interleavers with short blockchains. According to the symmetry concept, turbo codes consist of two symmetric convolutional codes preceded by an interleaver. Some...