Faculty Profiles - NOGAMI Yasuyuki

MISC - NOGAMI Yasuyuki

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On Derivation of Primitive Polynomials in the Case of (P^<P^<i+1>>-1)/(P^<P^i>-1) Prime

NOGAMI Y., MORIKAWA Y.

IEICE technical report. Information theory 99 ( 562 ) 31 - 35 2000.1

Language：Japanese Publisher：The Institute of Electronics, Information and Communication Engineers

In the area of information communication, Reed Solomon code(RS code)is often used to encode and decode per a byte. Therefore, RS code is defined over GF(2^8), a primitive polynomial of degree 8 over GF(2) is needed, so that a primitive polynomial of degree 2^i over GF(2). In this paper, Fermat prime is generalized into(P^P^<i+1>-1) / (P^P^i-1), where P is an arbitrary prime which includes P=2: Fermat prime. Then a method to derive primitive polynomials of degree P^<i+1>, P^<i+1> in the case of (P^P^<i+1>-1) / (P^P^i-1)prime is proposed. This method uses variable transformation;x:=x^P-x+s, s∈GF(P).

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Deriving infinite number of irreducible polynomials by repetition of variable transformations x:=x^P-x+s and x:=x^k

SAITO A., OKA H., NOGAMI Y., MORIKAWA Y.

IEICE technical report. Information theory 99 ( 562 ) 25 - 30 2000.1

Language：Japanese Publisher：The Institute of Electronics, Information and Communication Engineers

Two variable transformation methods are known to generate a number of irreducible polynomials; x:=x^k on condition of k-th power residue and x:=x^P-x on condition of trace. Those two transformations might not be consistent with each other owing to each conditions. In this paper, we consider the case of k|(P-1). Then we present a method to derive infinite number of irreducible polynomials of degree mk^jP^i from a irreducible polynomial of degree m by repetition of above variable transformations.

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A Consideration on Specifying Minimal Polynomials with nth Trace

NOGAMI Y., YAMANE N., MORIKAWA Y.

IEICE technical report. Information theory 99 ( 296 ) 7 - 11 1999.9

Deriving Infinite Number of Irreducible Polynomials by Variable Transformation x^p-x+s

THE TRANSACTIONS OF THE INSTITUTE OF ELECTRONICS, INFORMATION AND COMMUNICATION ENGINEERS A J82-A ( 4 ) 587 - 590 1999

Deriving Infinite Number of Irreducible Polynomials by Variable Transformation x^P-x+s

NOGAMI Yasuyuki, TANAKA Kiyoshi, SUGIMURA Tatsuo, OSHITA Shinjiro

The Transactions of the Institute of Electronics,Information and Communication Engineers. A J82-A ( 4 ) 587 - 590 1999

Deriving Infinite Number of Irreducible Polynomials by Variable Transformation x^p-x+s

NOGAMI Yasuyuki, TANAKA Kiyoshi, SUGIMURA Tatsuo, OSHITA Shinjiro

THE TRANSACTIONS OF THE INSTITUTE OF ELECTRONICS, INFORMATION AND COMMUNICATION ENGINEERS A J82-A ( 4 ) 587 - 590 1999

Deriving Infinite Number of Irreducible Polynomials by Variable Transformation x^P-x+s

NOGAMI Yasuyuki, TANAKA Kiyoshi, SUGIMURA Tatsuo, OSHITA Shinjiro

The Transactions of the Institute of Electronics,Information and Communication Engineers. A J82-A ( 4 ) 587-590 - 590 1999

A Consideration on Normal Bases over the Extension Fields of Prime Degree by P-Polynomials

NOGAMI Y., TANAKA K., SUGIMURA T., OSHITA S.

IEICE technical report. Information theory 97 ( 80 ) 25 - 30 1997.5

Language：Japanese Publisher：The Institute of Electronics, Information and Communication Engineers

In recent years, in the area of information security many considerations on the base of the finite field theory are proceeded. So considering finite fields into details is very interesting and important. In this paper, we consider on finite fields from the viewpoints of self recursive polynomials and P-polynomials. Consequently, in the extension field whose extension degree is a prime not its characteristic, normal bases and their minimal polynomials are determined uniquely. And the number of the normal bases over such extension fields is obtained. Furthermore, a new method to test for an irreducible polynomial whether a pair of its zeros is a normal base or not.

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原始多項式の判定および導出

電子情報通信学会論文誌 J79-A ( 3 ) 761 - 767 1996

Testing and Deriving Primitive Polynomial

THE TRANSACTIONS OF THE INSTITUTE OF ELECTRONICS, INFORMATION AND COMMUNICATION ENGINEERS A J79-A ( 3 ) 761 - 767 1996

Testing and Deriving Primitive Polynomial

THE TRANSACTIONS OF THE INSTITUTE OF ELECTRONICS, INFORMATION AND COMMUNICATION ENGINEERS A J79-A ( 3 ) 761 - 767 1996

原始多項式の判定および導出

野上保之, 杉村立夫

電子情報通信学会論文誌(A) 1996

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