On multiple caps in finite projective spaces
نویسندگان
چکیده
In this paper, we consider new results on (k, n)-caps with n > 2. We provide a lower bound on the size of such caps. Furthermore, we generalize two product constructions for (k, 2)-caps to caps with larger n. We give explicit constructions for good caps with small n. In particular, we determine the largest size of a (k, 3)-cap in PG(3, 5), which turns out to be 44. The results on caps in PG(3, 5) provide a solution to four of the eight open instances of the main coding theory problem for q = 5 and k = 4. Mathematics Subject Classification: 51E22, 94B05, 94B65
منابع مشابه
Complete caps in projective spaces PG ( n , q )
A computer search in the finite projective spaces PG(n, q) for the spectrum of possible sizes k of complete k-caps is done. Randomized greedy algorithms are applied. New upper bounds on the smallest size of a complete cap are given for many values of n and q. Many new sizes of complete caps are obtained. Mathematics Subject Classification (2000): 51E21, 51E22, 94B05.
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عنوان ژورنال:
- Des. Codes Cryptography
دوره 56 شماره
صفحات -
تاریخ انتشار 2010