Asymptotically good homological error correcting codes

Journal of Algebra Combinatorics Discrete Structures and Applications

article

Jason McCullough¹  Heather Newman² 

[1] Department of Mathematics, Iowa State University;Department of Mathematics, Drexel University

关键词: Error correcting codes;    Simplicial complexes;    Simplicial homology;   

DOI  :  10.13069/jacodesmath.617235

学科分类：社会科学、人文和艺术（综合）

来源: Yildiz Technical University

【 摘 要 】

Let ∆ be an abstract simplicial complex. We study classical homological error correcting codesassociated to ∆, which generalize the cycle codes of simple graphs. It is well-known that cyclecodes of graphs do not yield asymptotically good families of codes. We show that asymptoticallygood families of codes do exist for homological codes associated to simplicial complexes of dimensionat least 2. We also prove general bounds and formulas for (co-)cycle and (co-)boundary codes forarbitrary simplicial complexes over arbitrary fields.

【 授权许可】

CC BY