Self-Dual Codes and the (22,8,4) Balanced Incomplete Block Design
نویسنده
چکیده
We enumerate a list of 594 inequivalent binary (33, 16) doubly-even self-orthogonal codes that have no all-zero coordinates along with their automorphism groups. It is proven that if a (22, 8, 4) Balanced Incomplete Block Design were to exist then the 22 rows of its incident matrix will be contained in at least one of the 594 codes. Without using computers, we eliminate this possibility for 116 of these codes.
منابع مشابه
Hadamard matrices of order 36 and double-even self-dual [72,36,12] codes
A balanced incomplete block design (BIBD) [1] with parameters 2-(v, b, r, k, λ) (short 2-(v, k, λ)) is a pair (V,B) where V is a v-set (elements are called points) and B is a collection of b k-subsets (elements are called blocks) of V such that each point is contained in exactly r blocks and any pair of points is contained in exactly λ blocks. A Hadamard matrix of order n is an n × n (1,−1)-mat...
متن کاملTernary codes through ternary designs
It is known that under certain conditions the incidence matrix of a balanced incomplete block design (v, b, r, k, λ) gives a binary code of length b and size 2(v + 1). Here we investigate the conditions where a balanced ternary design gives a similar ternary code.
متن کاملConstruction and Performance Analysis of BIBD-QC-LDPC Codes for Correcting Erasure-Bursts
This paper presents a novel approach for constructing structured regular QC-LDPC codes based on a special type of combinatorial designs,known as the balanced incomplete block design (BIBD).The code design approach based on the technology of block cyclic shift and dispertion (BCSD) for correcting erasure-bursts over the binary bursts erasure channel (BBEC). Furthermore, the Tanner graph of the c...
متن کاملFingerprinting Codes for Internet-Based Live Pay-TV System Using Balanced Incomplete Block Designs
SUMMARY In recent years, with the rapid growth of the In-ternet as well as the increasing demand for broadband services, live pay-television broadcasting via the Internet has become a promising business. To get this implemented, it is necessary to protect distributed contents from illegal copying and redistributing after they are accessed. Fingerprinting system is a useful tool for it. This pap...
متن کاملCombinatorial Characterizations of Authentication Codes
In this paper, we prove two new combinatorial characterizations of authentication codes. Authentication codes without secrecy are characterized in terms of orthogonal arrays; and general authentication codes are characterized in terms of balanced incomplete block designs.
متن کامل