{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:43:29Z","timestamp":1753893809178,"version":"3.41.2"},"reference-count":0,"publisher":"The Electronic Journal of Combinatorics","issue":"1","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Electron. J. Combin."],"abstract":"<jats:p>For any odd prime power $q$ we first construct a certain non-linear binary code $C(q,2)$ having $(q^2-q)\/2$ codewords of length $q$ and weight $(q-1)\/2$ each, for which the Hamming distance between any two distinct codewords is in the range $[q\/2-3\\sqrt q\/2,\\ q\/2+3\\sqrt q\/2]$ that is, 'almost constant'. Moreover, we prove that $C(q,2)$ is distance-invariant. Several variations and improvements on this theme are then pursued. Thus, we produce other classes of binary codes $C(q,n)$, $n\\geq 3$, of length $q$ that have 'almost constant' weights and distances, and which, for fixed $n$ and big $q$, have asymptotically $q^n\/n$ codewords. Then we prove the possibility of extending our codes by adding the complements of their codewords. Also, by using results on Artin $L-$series, it is shown that the distribution ofthe $0$'s and $1$'s in the codewords we constructed is quasi-random.  Our construction uses character sums associated with the quadratic character $\\chi$ of $F_{q^n}$ in which the range of summation is $F_q$. Relations with the duals of the double error correcting BCH codes and the duals of the Melas codes are also discussed.<\/jats:p>","DOI":"10.37236\/1228","type":"journal-article","created":{"date-parts":[[2020,1,11]],"date-time":"2020-01-11T01:50:34Z","timestamp":1578707434000},"source":"Crossref","is-referenced-by-count":1,"title":["On a Class of Constant Weight Codes"],"prefix":"10.37236","volume":"3","author":[{"given":"Mihai","family":"Caragiu","sequence":"first","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[1996,1,2]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v3i1r4\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v3i1r4\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,18]],"date-time":"2020-01-18T06:18:21Z","timestamp":1579328301000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v3i1r4"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1996,1,2]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[1996,1,1]]}},"URL":"https:\/\/doi.org\/10.37236\/1228","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[1996,1,2]]},"article-number":"R4"}}