[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-31282":3,"doc-seo-31282":26},{"code":4,"msg":5,"data":6},0,"success",{"doc_id":7,"user_id":8,"nickname":9,"user_avatar":10,"doc_module":4,"category_id":11,"category_name":12,"doc_title":13,"doc_description":14,"file_id":15,"file_url":16,"file_type":17,"file_size":18,"view_count":19,"is_deleted":4,"is_public":19,"is_downloadable":19,"audit_status":19,"page_count":20,"language":21,"table_of_contents":22,"faqs":23,"seo_title":13,"seo_description":14,"update_tm":24,"read_time":25},31282,7971461741311,"Ophelia","https://ap-avatar.wpscdn.com/avatar/74000253aff267980c6?x-image-process=image/resize,m_fixed,w_180,h_180&k=1779345379180704826",6,"Technology","Fundamentals of Error-Correcting Codes","Fundamentals of Error-Correcting Codes provides a rigorous introduction to coding theory from both engineering and mathematical perspectives. It covers classical foundations such as linear codes, generator and parity-check matrices, dual codes, weights and distances, and standard constructions for creating new codes. The text extends to modern techniques from specialized literature, including bounds on code size, finite fields, cyclic codes, and major decoding methods for BCH and Reed–Solomon codes, supported by numerous examples and exercises.","cbCaibfVHerZIJgo","https://ap.wps.com/l/cbCaibfVHerZIJgo","pdf",3565729,1,665,"English","# Preface\n# Basic concepts of linear codes\n## Three fields\n## Linear codes, generator and parity check matrices\n## Dual codes\n## Weights and distances\n## New codes from old\n## Permutation equivalent codes\n## More general equivalence of codes\n## Hamming codes\n## The Golay codes\n## Reed–Muller codes\n## Encoding, decoding, and Shannon’s Theorem\n## Sphere Packing Bound, covering radius, and perfect codes\n# Bounds on the size of codes\n## Aq(n,d) and Bq(n,d)\n## The Plotkin Upper Bound\n## The Johnson Upper Bounds\n## The Singleton Upper Bound and MDS codes\n## The Elias Upper Bound\n## The Linear Programming Upper Bound\n## The Griesmer Upper Bound\n## The Gilbert Lower Bound\n## The Varshamov Lower Bound\n## Asymptotic bounds\n# Finite fields\n## Polynomials and the Euclidean Algorithm\n## Primitive elements\n## Constructing finite fields\n# Cyclic codes\n## Factoring xn − 1\n## Basic theory of cyclic codes\n## Zeros of a cyclic code\n## Meggitt decoding of cyclic codes\n# BCH and Reed–Solomon codes\n## BCH codes\n## Reed–Solomon codes\n## Decoding BCH codes\n# Duadic codes","[{\"question\":\"What perspectives does the book use to teach coding theory?\",\"answer\":\"The book introduces coding theory from both an engineering viewpoint and a mathematical viewpoint, aiming to serve readers with different backgrounds.\"},{\"question\":\"Which foundational topics are covered in the early chapters?\",\"answer\":\"It covers basic linear-code structures such as generator and parity-check matrices, dual codes, weights and distances, and several methods for constructing new codes from existing ones.\"},{\"question\":\"What later topics does the book cover beyond linear codes?\",\"answer\":\"Later sections include bounds on code size, finite fields, cyclic codes and their decoding, and BCH and Reed–Solomon codes with multiple decoding algorithms.\"}]",1779224654,1676,{"code":4,"msg":27,"data":28},"ok",{"site_id":29,"language":30,"slug":31,"title":13,"keywords":32,"description":14,"schema_data":33,"social_meta":85,"head_meta":87,"extra_data":89,"updated_unix":24},105,"en","fundamentals-of-error-correcting-codes","",{"@graph":34,"@context":84},[35,52,67],{"@type":36,"itemListElement":37},"BreadcrumbList",[38,42,46,49],{"item":39,"name":40,"@type":41,"position":19},"https://docshare.wps.com","Home","ListItem",{"item":43,"name":44,"@type":41,"position":45},"https://docshare.wps.com/document/","Document",2,{"item":47,"name":12,"@type":41,"position":48},"https://docshare.wps.com/document/technology/",3,{"item":50,"name":13,"@type":41,"position":51},"https://docshare.wps.com/document/fundamentals-of-error-correcting-codes/31282/",4,{"url":50,"name":13,"@type":53,"author":54,"headline":13,"publisher":56,"fileFormat":59,"description":14,"dateModified":60,"datePublished":61,"encodingFormat":59,"isAccessibleForFree":62,"interactionStatistic":63},"DigitalDocument",{"name":9,"@type":55},"Person",{"url":39,"name":57,"@type":58},"DocShare","Organization","application/pdf","2026-05-20","2026-05-19",true,{"@type":64,"interactionType":65,"userInteractionCount":19},"InteractionCounter",{"@type":66},"ViewAction",{"@type":68,"mainEntity":69},"FAQPage",[70,76,80],{"name":71,"@type":72,"acceptedAnswer":73},"What perspectives does the book use to teach coding theory?","Question",{"text":74,"@type":75},"The book introduces coding theory from both an engineering viewpoint and a mathematical viewpoint, aiming to serve readers with different backgrounds.","Answer",{"name":77,"@type":72,"acceptedAnswer":78},"Which foundational topics are covered in the early chapters?",{"text":79,"@type":75},"It covers basic linear-code structures such as generator and parity-check matrices, dual codes, weights and distances, and several methods for constructing new codes from existing ones.",{"name":81,"@type":72,"acceptedAnswer":82},"What later topics does the book cover beyond linear codes?",{"text":83,"@type":75},"Later sections include bounds on code size, finite fields, cyclic codes and their decoding, and BCH and Reed–Solomon codes with multiple decoding algorithms.","https://schema.org",{"og:url":50,"og:type":86,"og:title":13,"og:site_name":57,"og:description":14},"article",{"robots":88,"canonical":50},"index,follow",{"doc_id":7,"site_id":29}]