Distance-Regular Graphs

algorithmics and modular computations, Theory of Codes and Cryptography (3).From an analytical 1. RE Blahut. Theory and practice of error control codes. eecs.uottawa.ca/∼yongacog/courses/coding/ (3) R.E. Blahut,Theory and Practice of Error Control Codes, Addison Wesley, 1983. QA 268. Cached. Download as a PDF 457, Theory and Practice of Error Control CodesBlahut 1984 (Show Context). Citation Context..ontinued fractions.

Theory and practice of error control codes

A classical method of constructing a linear code over $ {\mathrm {GF}}(q)$ with a $t$ -design is to use the incidence matrix of the $t$ -design as a generator matrix over $ {\mathrm {GF}}(q)$ of the code. This approach has been extensively investigated in the literature. In this paper, a different method of constructing linear codes using specific classes of 2-designs is studied, and linear codes with a few weights are obtained from almost difference sets, difference sets, and a type of 2-designs associated to semibent functions. Two families of the codes obtained in this paper are optimal. The linear codes presented in this paper have applications in secret sharing and authentication schemes, in addition to their applications in consumer electronics, communication and data storage systems. A coding-theory approach to the characterization of highly nonlinear Boolean functions is presented.

Linear Codes From Some 2-Designs

A classical method of constructing a linear code over $\gf(q)$ with a $t$-design is to use the incidence matrix of the $t$-design as a generator matrix over $\gf(q)$ of the code. This approach has been extensively investigated in the literature. In this paper, a different method of constructing linear codes using specific classes of $2$-designs is studied, and linear codes with a few weights are obtained from almost difference sets, difference sets, and a type of $2$-designs associated to semibent functions. Two families of the codes obtained in this paper are optimal. The linear codes presented in this paper have applications in secret sharing and authentication schemes, in addition to their applications in consumer electronics, communication and data storage systems. A coding-theory approach to the characterisation of highly nonlinear Boolean functions is presented.

Linear Codes from Some 2-Designs

Locally decodable codes (LDCs) allow one to decode any particular symbol of the input message by making a constant number of queries to a codeword, even if a constant fraction of the codeword is damaged In a recent work [J ACM, 55 (2008), article 1], Yekhanin constructs a 3-query LDC with subexponential length However, this construction requires a conjecture that there are infinitely many Mersenne primes In this paper, we give the first unconditional constant query LDC construction with subexponential codeword length In addition, our construction reduces codeword length

3-Query Locally Decodable Codes of Subexponential Length.

Codebooks (also called signal sets) meeting the Welch bound on the maximum correlation amplitude are called MWBE codebooks and are desirable in code-division multiple-access systems. Two different but related constructions of MWBE codebooks from difference sets were developed by Xia and Ding recently. The objectives of this correspondence are to present a generic construction of MWBE codebooks that contains the previous two constructions as special cases and describe new MWBE codebooks that cannot be produced by the earlier two constructions.

A Generic Construction of Complex Codebooks Meeting the Welch Bound

In 1976, Helleseth conjectured that two binary m-sequences of length 2 m ? 1 can not have a three-valued crosscorrelation function when m is a power of 2. We show that this conjecture is true when ?1 is a correlation value. In other words, if $${{\mathcal{C}}_{1,k}}$$ is the cyclic code of length 2 m ? 1 with two zeros ?, ? k , where ? is a primitive element of $${{\mathbb{F}}_{2^m}}$$ and gcd(k, 2 m ? 1) = 1, then its dual $${{\mathcal{C}}_{1,k}^{\perp}}$$ can not have three weights when m is a power of 2.

On cyclic codes of length $${2^{2^r}-1}$$ with two zeros whose dual codes have three weights

Strongly regular graphs associated with ternary bent functions

Cameron-Liebler line classes with parameter x = q 2 - 1 2

In direct spread CDMA systems, codebooks meeting the Welch bounds are used to distinguish among the signals of different users. Recently, constructions of codebooks with difference sets meeting Welch's bound on the maximum cross-correlation amplitude were developed. In this paper, a generic construction of codebooks using almost difference sets is considered and several classes of codebooks nearly meeting the Welch bound are obtained. The parameters of the codebooks constructed in this paper are new.

Tao Feng

Papers

A Generic Construction of Complex Codebooks Meeting the Welch Bound

On cyclic codes of length $${2^{2^r}-1}$$ with two zeros whose dual codes have three weights

Strongly regular graphs associated with ternary bent functions

Cameron-Liebler line classes with parameter x = q 2 - 1 2

Codebooks from almost difference sets