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The construction of the tables was based on linear recurring sequences over GF[2]. For each degree n, the polynomials are sorted with respect to their periods. Each polynomial is listed in octal representation with period and decimation. In the present tables, all irreducible polynomials over GF[2] are given, with the period of their roots and its "decimation" (cf. below), from degree 10 through degree 20. Polynomials are listed in octal representation, such that each octal digit represents three binary digits. In the binary representation of the leftmost octal digit, the first 1 from the left is the coefficient of as*. The binary equivalent of 2527 is 010101010111, and the corresponding polynomial is thus x10 + xs + x6 + x* + x2 + xl + 1. Of any pair consisting of a polynomial and its reciprocal polynomial, only that one is listed which has the smaller binary number representation. For each degree n, the polynomials are sorted with respect to their periods, beginning with the primitive polynomials, of period 2" — 1. Within each period, the polynomials are arranged in lexicographical order. The decimation stands to the left of the octal representation. For given degree n, the possible periods e are the divisors of 2" — 1, such that 2 belongs to the exponent n (mod e). For given e, the number of different irreducible polynomials of degree n and period e is <p(e)/n. These polynomials are either all symmetric (self-reciprocal) or all nonsymmetric. Preceding the tables, the possible periods e are listed for each n, together with the numbers <p(e)/n. Since only one of a nonsymmetric polynomial and its reciprocal polynomial is given, the tables contain only %<p(e)/n polynomials in the nonsymmetric cases. The page indexing uses a double decimal number, where the first part shows the degree n. The construction of the tables was based on linear recurring sequences over GF[2]. We describe the construction in the notation of Selmer [4]. For each degree n, one primitive polynomial /(x) was chosen to represent the -decimation 1. If 1(a) = 0, a <= GF[2"], all the roots of f(x) are given by a2i, i = 0, 1, • • • , n 1. The linear recurrence relation with characteristic polynomial f(x) generates binary maximal recurring sequences (st) = s0, su s2, ■ ■ ■ . With an appropriate starting point, we get the "power sum sequence" (s,), defined by Received November 12, 1971. AMS 1970 subject classifications. Primary 12C05, 12C10, 12-04.

Table of irreducible polynomials over 𝐺𝐹[2] of degrees 10 through 20