Heise, W. Topics in algebraic coding theory. (English) Zbl 0708.94013 Geometries, codes and cryptography, CISM Courses Lect. 313, 77-99 (1990). [For the entire collection see Zbl 0699.00030.] A wide range of topics in algebraic coding theory is surveyed. Starting with the definition of a code, Heise discusses bounds on the size of a code, cyclic, BCH, Goppa, Hamming, MDS, and RM codes, McEliece’s cryptosystem based on Goppa codes, the connection between MDS codes and geometries and the automorphism group of a code. All this is done in a mere fifteen pages: very fast for the non-expert, while the expert will find little news. The last chapter is entirely devoted to QR-codes. It includes the Golay codes, the Gleason-Prange theorem (on the automorphism group of a QR code) and the square root bound (on the minimum distance of a QR code). A recent improvement on the square root bound is stated and proved. It applies to QR codes of length \(n=3\) (mod 4) over a prime field GF(p) with \(p=3\) (mod 4). This improvement might be unknown to quite a few people. Reviewer: L.M.G.M.Tolhuizen Cited in 1 Document MSC: 94B05 Linear codes (general theory) 94B65 Bounds on codes Keywords:geometry; cryptography; algebraic coding theory; bounds; QR-codes; Golay codes; Gleason-Prange theorem; square root bound Citations:Zbl 0699.00030 PDFBibTeX XML