Construction of the codes (2M, M+1, 2M-1), with M ≥ 3,
using lexicographical blocks

Francisco Antonio de ALENCAR MENEZES[1]

Elvio César GIRAUDO[2]

§    ABSTRACT: Concepts related to the theory of the linear codification are presented to the new construction of lexicographical codes, and to propose for the code (8, 4, 4), a lexicographic construction for matrices or for lexicographical blocks. The construction starts from the generating matrix, whose code words are at same Hamming distance and the same Euclidean distance, two by two. A fundamental property is that the code's parity check matrix is the transposed one of its generating matrix, what hints to the Hamming code differentiated decode procedure. In this context the family of codes of parameters is defined (2M, M+1, 2M-1), with     M ≥ 3. Curves of bit error rate are present for this code in a PSK digital modulation system.

§    KEYWORDS: Lexicographic code; linear code; error correction code.


[1] Centro de Ciências Exatas e Tecnologia, Coordenação de Ciências-Matemática, Universidade Estadual Vale do Acaraú, CEP: 62.040-370, Sobral, Ceará, Brasil, E‑mail:

[2] Departamento de Engenharia de Teleinformática, Centro de Tecnologia, Universidade Federal do Ceará – UFCE, Caixa Postal 6007, CEP: 60.455-760, Fortaleza, Ceará, Brasil, E‑mail: