Open AccessNew Quantum and LCD Codes over Finite Fields of Even Characteristic
Author(s) -
Habibul Islam,
Om Prakash
Publication year - 2021
Publication title -
defence science journal/defence science journal
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.198
H-Index - 32
eISSN - 0976-464X
pISSN - 0011-748X
DOI - 10.14429/dsj.71.16641
Subject(s) - liquid crystal display , mathematics , code (set theory) , linear code , commutative property , discrete mathematics , euclidean geometry , computer science , algorithm , block code , geometry , programming language , decoding methods , operating system , set (abstract data type)
For an integer m ≥ 1, we study cyclic codes of length l over a commutative non-chain ring F2m + uF2m , where u2 = u . With a new Gray map and Euclidean dual-containing cyclic codes, we provide many new and superior codes to the best-known quantum error-correcting codes. Also, we characterise LCD codes of length l with respect to their generator polynomials and prove that F2m − image of an LCD code of length l is an LCD code of length 2l . Finally, we provide several optimal LCD codes from the Gray images of LCD codes over F2m + uF2m .