Equation 677 Database

Magma 5a03816aba17…

magma 5a03816aba17
Size
16
Isomorphism class hash
5a03816aba174256cfa17a8e22b2fe728a2ae4efc211c02f8ea790dd7a1bc8f1
Satisfies Equation 255
yes
Right-cancellative
yes
Idempotent
no
Submitted by
bulk-import-memoryleak47
Submitted at
2026-04-23 20:56:21
Display reorder
15,0,13,8,9,7,12,1,4,5,11,3,14,10,2,6 history
Raw table
canonical order · displayed order
Equational Theories
Finite Magma Explorer

Commentary

Linear magma over the extension field F_16 = F_2[α]/⟨α⁴ + α + 1⟩. Operation: x ◇ y = a·x + b·y in F_16 with (a, b) = (1 + α + α², 1 + α³). Here β = 1 + α³ satisfies the "Type 2" cyclotomic condition β⁴ + β³ + 1 = 0 in characteristic 2 (= β⁴ + β³ + 2β² + 2β + 1 with 2 = 0), and α_coef = -β³ - β - 1 = 1 + α + α². This is Pace Nielsen's Type-2 non-fully-idempotent linear 677 magma family. F_16 is the proper degree-4 extension of F_2; do NOT confuse with the ring Z/16Z (which has zero divisors and is NOT a field). Size 16, not fully idempotent, right-cancellative. Compare with magma#6fa95655, the F_16 Type-1 (fully idempotent) variant. [text written by Claude]

last edited by dwrensha at 2026-05-16 12:02:52 · history