Choi, Soohak; Hyun, Jong Yoon; Kim, Hyun Kwang Local duality theorem for \(q\)-ary 1-perfect codes. (English) Zbl 1323.94155 Des. Codes Cryptography 70, No. 3, 305-311 (2014). Summary: In this paper, we derive the relationship between local weight enumerator of \(q\)-ary 1-perfect code in a face and that in the orthogonal face. As an application of our result, we compute the local weight enumerators of a shortened, doubly-shortened, and triply-shortened \(q\)-ary 1-perfect code. Cited in 3 Documents MSC: 94B05 Linear codes (general theory) Keywords:\(q\)-ary 1-perfect code; local weight enumerator; local duality theorem PDFBibTeX XMLCite \textit{S. Choi} et al., Des. Codes Cryptography 70, No. 3, 305--311 (2014; Zbl 1323.94155) Full Text: DOI References: [1] Etzion T., Vardy A.: Perfect binary codes: constructions, properties, and enumeration. IEEE Trans. Inform. Theory 40(3), 754-763 (1994) · Zbl 0824.94029 · doi:10.1109/18.335887 [2] Hyun J.Y.: Generalized MacWilliams identities and their applications to perfect binary codes. Des. Codes Cryptogr. 50(2), 173-185 (2009) · Zbl 1237.94125 · doi:10.1007/s10623-008-9222-6 [3] Krotov D.S.: On weight distributions of perfect colorings and completely regular codes. Des. Codes Cryptogr. 61(3), 315-329 (2011) · Zbl 1235.94065 · doi:10.1007/s10623-010-9479-4 [4] MacWilliams F.J., Sloane N.J.: The Theory of Error-Correcting Codes. North-Holland, Amsterdam (1998) · Zbl 0369.94008 [5] Vasil’eva A.Y.: Local spectra of perfect binary codes. Russian translations. II. Discret. Appl. Math. 135(1-3), 301-307 (2004) · Zbl 0930.94045 · doi:10.1016/S0166-218X(02)00313-X This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.